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Instituto Superior Técnico


The research is aimed at the study of various classes of operators ranging from classical Cauchy-type operators to abstract Toeplitz operators and pseudo-differential operators. The work includes both the analysis of operators as mappings between function spaces and the study of Banach algebras of these operators. Typical applications in this area include wave scattering in models involving mixed media.

Research topics:

  • Operator Algebras of non local type and factorization of oscillatory symbols
  • Operator Normalization and boundary-value problems
  • Symbol Factorization and application to integrable systems
  • Non associative algebras
  • Approximation methods in operator algebras
Seminar: Functional Analysis and Applications

Members

M. Amélia Bastos
António Bravo
M. Cristina Câmara
Catarina Carvalho
António Ferreira dos Santos (coordinator)
Alexei Yu. Karlovich
Amarino Lebre
Paulo Lopes
Helena Mascarenhas
Lina Oliveira
Ana Moura Santos
Pedro Alexandre Santos
Frank-Olme Speck
Francisco Sepúlveda Teixeira
Gueorgui Litvinchuk : Universidade da Madeira
Students

Nuno António, Maria João Pereira Braga, Cristina Diogo, Claúdio Fernandes, Jorge Ferreira, Maria do Carmo Martins, Sofia Naique, Maurício Reis, Isabel Oliveira, Luís Pessoa


Books
  • I. Gohberg, A.F. dos Santos, F.-O. Speck, F.S. Teixeira, W. Wendland (Editors). Operator Theoretical Methods and Applications to Mathematical Physics. The Erhard Meister Memorial Volume. Operator Theory: Advances and Applications, Vol. 147, Birkhäuser, Basel 2004, xvi + 476 p.
  • A. Böttcher, A.F.dos Santos, M.A. Kaashoek, A. Lebre, F.-O. Speck (Editors). Singular Integral Operators, Factorization and Applications. Proceedings IWOTA Conf. Portugal 2000. Operator Theory: Advances and Applications, Vol. 142, 404 p., Birkhäuser, Basel 2003.
  • I. Gohberg, N. Manojlovic and A. F. dos Santos (Editors). Factorization and Integrable Systems, Vol. 141, Operator Theory: Advances and Applications. Birkhäuser, 2003.
  • S. Samko, A.Lebre and A.F. dos Santos (Editors). Factorization. Singular Operators and Related Problems. Proceedings of the Conference in Honour of Professor Gueirgii Litvinchuk. Kluwer, 2003.
  • G. S. Litvinchuk. Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift, Vol. 523, Mathematics and its Applications. Kluwer Academic Publisher, 2000.


  • Research Papers


  • 2004
    • A. Bastos, A. Bravo and Yu. I. Karlovich, Convolution Type Operators with Symbols generated by slow oscillating and piecewise continuous matrix functions. Operator Theory: Advances and Applications. Vol 147, 151--174, Birkhäuser, Basel, 2004.
    • L. Castro, F.-O. Speck and F.S. Teixeira, On a class of wedge diffraction problems posted by Erhard Meister. Operator Theoretical Methods and Applications to Mathematical Physics. The Erhard Meister Memorial Volume (Eds. I. Gohberg et alt.), Operator Theory: Advances and Applications, Vol. 147,  211--238. Birkhäuser, Basel 2004.
    • A. Karlovich, Norms of Toeplitz and Hankel operators on Hardy type subspaces of rearrangement-invariant spaces. Integral Equations and Operator Theory, 49 (2004), no. 1, in print.
    • A. Karlovich, Some algebras of functions with Fourier coefficients in weighted Orlicz sequence spaces. Operator Theoretical Methods and Applications to Mathematical Physics. Erhard Meister Memorial Volume. Operator Theory: Advances and Applications, 147 (2004), 287 -- 296.
    • F.-O. Speck, In Memory of Erhard Meister (a short biography).  Operator Theoretical Methods and Applications to Mathematical Physics. The Erhard Meister Memorial Volume (Eds. I. Gohberg et al.). Operator Theory: Advances and Applications, Vol. 147, Birkhäuser, Basel, 2004, 27--46.

    •  
  • 2003
  • M. A. Bastos, Yu. I. Karlovich and A.F. dos Santos. Oscillatory Riemann-Hilbert problems and the corona theorem.  J. Funct. Anal., Vol. 197, 347--397, 2003.
  • A. Bastos, A. Bravo and Yu. I. Karlovich, Singular Integral Operators with Piecewise Almost Periodic Coefficients and Carleman Shift. Singular Integral Operators, Factorization and Applications, (Eds. A. Böttcher et alt.). Proceedings IWOTA Conf. Portugal 2000, Operator Theory: Advances and Applications, vol. 142, 29--57, Birkhäuser, Basel 2003.
  • L. Castro, F.-O. Speck and F.S. Teixeira, Explicit solution of a Dirichlet-Neumann wedge diffraction problem with a strip. Journal of Integral Equations and Applications 15 (2003), 359--383.
  • L. Castro and F.-O. Speck, Well-posedness of diffraction problems involving n coplanar strips. Singular Integral Operators, Factorization and Applications (Eds. A. Böttcher et alt.). Proceedings IWOTA Conf. Portugal 2000, Operator Theory: Advances and Applications, Vol. 142, 81--93, Birkhäuser, Basel 2003.
  • L. Castro, R. Duduchava and F.-O. Speck, Localization and minimal normalization of some basic mixed boundary value problems. Factorization, Singular Operators and Related Problems. Proceedings of the Conference in Honour of Professor Georgii Litvinchuk at Funchal, Portugal 2002 (Eds. S. Samko et alt.),  73--100, Kluwer, Dordrecht 2003.
  • A. Conceição, V.G. Kravchenko and F.S. Teixeira. Factorization of matrix functions and the resolvents of certain operators. Operator Theory:Advances and Applications, Vol.142,  91--100. Birkhäuser Verlag, 2003.
  •  A. Conceição, V.G. Kravchenko, and F.S. Teixeira. Factorization of some classes of matrix functions and the resolvent of a Hankel operator. Factorization, Singular Operators and Related Problems,  101--110. Kluwer Academic Publishers, 2003.
  • A. Karlovich, Fredholmness of singular integral operators with piecewise continuous coefficients on weighted Banach function spaces. Journal of Integral Equations and Applications, 15 (2003), no. 3,  263--320.
  • A. Karlovich,  Yu. Karlovich, and A. Lebre, Invertibility of functional operators with slowly oscillating non-Carleman shifts. Singular Integral Operators, Factorization and Applications. International Workshop on Operator Theory and Applications, IWOTA 2000, Portugal. Operator Theory: Advances and Applications, 142 (2003), 147--174.
  • A. Karlovich and Yu. Karlovich, Compactness of commutators arising in the Fredholm theory of singular integral operators with shifts. Factorization, Singular Operators and Related Problems; Proceedings of the conference in honour of Georgui Litvinchuk, Kluwer Academic Publishers, Dordrecht, 2003,  111--129.
  • V. G. Kravchenko, A. B. Lebre and J. Rodriguez. Factorization of singular integral operators with shift via factorization of matrix functions. Operator Theory: Advances and Applications, Vol. 142, 189--211. Birkhäuser, 2003.
  •  P.A. Santos and B. Silbermann. An axiomatic approach to stability of approximation sequences. In:Singular Integral Operators, Factorization and Applications, (Eds. A. Böttcher et alt.). Proceedings IWOTA Conf. Portugal 2000, Operator Theory: Advances and Applications, Vol. 142, 369--381. Birkhäuser, Basel 2003.
  • 2002
  • M. A. Bastos, Yu. I. Karlovich and A.F. dos Santos. The invertibility of convolution type operators on a union of intervals and the corona theorem. Integral Equations Operator Theory, 42(1),  22--56, 2002.
  • M. C. Câmara, A.F. dos Santos and M.P. Carpentier. Explicit Wiener-Hopf factorization and non-linear Riemann-Hilbert problems.  Proc. Roy. Soc. Edinburgh, Ser. A, 132, 45--74, 2002.
  • L.P. Castro, R. Duduchava, and F.-O. Speck. Singular integral equations on piecewise smooth curves in spaces of smooth functions. Toeplitz Matrices and Singular Integral Equations (A. Bottcher et al., editor). Operator Theory: Advances and Applications, vol 135, 107--144. Birkhauser, 2002.
  • T. Ehrhardt and F.-O. Speck. Transformation techniques towards the factorization of non-rational 2 x 2 matrix functions. Linear Algebra Appl., 353,  53--90, 2002.
  • A. Yu. Karlovich. Algebras of singular integral operators on rearrangement-invariant spaces and Nikolski ideals.  New York Journal of Mathematics, 8,  215--234, 2002.
  • A. Yu. Karlovich. Algebras of singular integral operators with PC coeffcients in rearrangement-invariant spaces with Muckenhoupt weights. J. Operator Theory, 47,  303--323, 2002.
  • A. Yu. Karlovich and Yu. I. Karlovich. Invertibility in Banach algebras of functional operators with non-carleman shifts. Proceedings of Ukrainian Mathematical Congress - 2001, 107--124. Institute of Mathematics of NAS of Ukraine, Kiev, 2002.
  • A. Yu. Karlovich and Yu. I. Karlovich. One-sided invertibility of binomial functional operators with a shift on rearrangement-invariant spaces.Integral Equations Operator Theory, 42(2), pp. 201--228, 2002.
  • F.-O. Speck. In Memoriam Professor Erhard Meister (1930-2001). Math. Methods Appl.Sci., 25, 1--2, 2002.
  • 2001
  • M. C. Câmara, A. F. dos Santos, and N. Manojlovic. Generalized factorization for NxN Daniele-Khrapkov matrix functions. Math. Methods Appl. Sci., 24,  993--1020, 2001.
  • A. Yu. Karlovich. Criteria for one-sided invertibility of a functional operator in rearrangement-invariant spaces of fundamental type.  Math. Nachr., 229,  91--118, 2001.
  • Yu. I. Karlovich and A. B. Lebre. Algebra of singular integral operators with a Carleman backward slowly oscillating shift. Integral Equations Operator Theory, 41,  288--323, 2001.
  • A. Yu. Karlovich and L. Maligranda. On the interpolation constant for Orlicz spaces. Proc. Amer. Math. Soc., 129, 2727--2739, 2001.
  • V. G. Kravchenko, A. B. Lebre, and G. S. Litvinchuck. Spectrum problems for singular integral operators with Carleman shift. Math. Nachr., 226, 129--151, 2001.
  • V.G. Kravchenko, A.B. Lebre and J.S. Rodriguez. Factorization of singular integral operators with a Carleman shift and spectral problems. J. Integral Equations Appl., 13(4), 339--383, 2001 (published in 2002).
  • P. A. Santos. Spline approximation methods with uniform meshes in algebras of multiplication and convolution operators. Math. Nachr., 232, 95--127, 2001.
  • 2000
  • A. Böttcher, Y. I. Karlovich, and V. S. Rabinovich. The method of limit operators for one-dimensional integrals with slowly oscillating data. J. Operator Theory., 43, 171--198, 2000.
  • M. C. Câmara and A. F. dos Santos. Wiener-Hopf factorization for a class of oscillatory symbols. Integral Equations Operator Theory, 36(4), 409--432, 2000.
  • L. P. Castro and F.-O. Speck. An operator approach to a boundary value problem for the Helmholtz equation. Proceedings of the 17th Conference on Operator Theory at Timisoara, Romenia, June 1998, Theta Foundation,  67--86, 2000.
  • L. P. Castro and F.-O. Speck. Relations between convolution type operators on intervals and on the half-line. Integral Equations Operator Theory, 37, 169--207, 2000.
  • R. Duduchava and F.-O. Speck. Singular integral equations in special weighted spaces. Georgian Math. J., 7, 633-642, 2000.
  • A. Karlovich, On the essential norm of the Cauchy singular integral operator in weighted rearrangement-invariant spaces. Integral Equations and Operator Theory, 38, no. 1, 28--50, 2000.
  • P. A. Lopes and A. F. dos Santos. New results on the invertibility of the finite interval convolution operator.Integral Equations Operator Theory, 38, 317--333, 2000.
  • P. A. Santos and B. Silbermann. Galerkin method for Wiener-Hopf operators with piecewise continuous symbol. Integral Equations Operator Theory, 38, 66--80, 2000.
  • 1999
  • M. C. Câmara and A. F. dos Santos. Wiener-Hopf factorization of a generalized Daniele-Krapkov class of 2x2 matrix symbols. Math. Methods Appl. Sci., 22(6), 461--484, 1999.
  • Y. I. Karlovich, I. M. Spitkovsky, and R. A. Walker. Almost periodic factorization of block triangular matrix functions revisited. Linear Algebra Appl., 293(1-3), 199--232, 1999.
  • F. Penzel and F. S. Teixeira. The Helmholtz equation in a quadrant with Robin's conditions. Math. Methods Appl. Sci., 22(3), 201--216, 1999.
  • 1998
  • M. A. Bastos, Yu. Karlovich, A. F. dos Santos, and P. M. Tishin. The corona theorem and the existence of canonical factorization of triangular AP-matrix functions. J. Math. Anal. Appl., 223, 494--522, 1998.
  • M. A. Bastos, Yu. Karlovich, A. F. dos Santos, and P. M. Tishin. The corona theorem and the canonical factorization of triangular AP-matrix functions - effective criteria and explicit formulas. J. Math. Anal. Appl., 223, 523--550, 1998.
  • J. A. Ball, Y. I. Karlovich, L. Rodman, and I. M. Spitkovsky. Sarason interpolation and Toeplitz corona theorem for almost periodic matrix functions. Integral Equations Operator Theory, 32, 243--281, 1998.
  • M. A. Bastos, Yu. Karlovich, I. M. Spitkovsky, and P. M. Tishin. On a new algorithm for almost periodic factorization.  Recent Progress in Operator Theory, I. Gohberg, R. Mennicken, and C. Tretter, editors, vol. 103, Operator Theory: Advances and Applications,  53--74. Birkhäuser, 1998.
  • A. Böttcher and Y. I. Karlovich. Algebra of singular integral operators on the Lebesgue space with a Muckenhoupt weight on a closed Carleson curve. Dokl. Math., 57, 193--196, 1998.
  • A. Böttcher, Y. I. Karlovich, and V. S. Rabinovich. Mellin pseudodifferential operators with slowly varying symbols and singular integrals on Carleson curves with Muckenhoupt weights. Manuscripta Math., 95, 363--376, 1998.
  • M. C. Câmara and A. F. dos Santos. A non-linear approach to generalized factorization of matrix functions. Differential and Integral Operators,  I. Gohberg, R. Mennicken, and C. Tretter, editors, volume 102 of Operator Theory: Advances and Applications,  21--37. Birkhäuser, 1998.
  • L. P. Castro and F.-O. Speck. A Fredholm study for Sommerfeld diffraction problems. In M. Bach, C. Constanda, G. C. Hsiao, A.-M. Sändig, and P. Werner, editors, Analysis, Numerics and Applications of Differential and Integral Equations, Proc. Inter. Conf. Stuttgart 1996, vol. 379, Pitman Research Notes in Math.,  47--51. Addison Wesley Longman, 1998.
  • L. P. Castro and F.-O. Speck. Regularity properties and generalized inverses of delta-related operators. Z. Anal. Anwendungen, 17, 577--598, 1998.
  • Y. I. Karlovich and I. M. Spitkovsky. The semi-Fredholmness of singular integral operators with matrix semi-almost periodic coefficients. Dokl. Math., 57, 176--178, 1998.
  • E. Meister, F. Penzel, F.-O. Speck, and Teixeira F. S. Some interior and exterior boundary value problems for the Helmholtz equation in a quadrant. In I. Gohberg, R. Mennicken, and C. Tretter, editors, Differential and Integral Operators, vol. 102,  Operator Theory: Advances and Applications, 169--178. Birkhäuser, 1998.
  • A. Moura Santos, F.-O. Speck, and F. S.Teixeira. Minimal normalization of Wiener-Hopf operators in applications. In M. Bach, C. Constanda, G. C. Hsiao, A.-M. Sändig, and P. Werner, editors, Analysis, Numerics and Applications of Differential and Integral Equations, Proc. Intern. Conf. Stuttgart 1996, vol. 379, Pitman Research Notes in Math.,189--193. Addison Wesley Longman, 1998.
  • A. Moura Santos, F.-O. Speck, and F. S.Teixeira. Minimal normalization of Wiener-Hopf operators in spaces of Bessel potentials. J. Math. Anal. Appl., 225, 501--531, 1998.
  • 1997
  • A. Böttcher and Y. I. Karlovich. The algebra of singular integral operators on a closed Carleson curve. Dokl. Math., 56, 813--816, 1997.
  • L. P. Castro and F.-O. Speck. A Fredholm study for convolution operators with piecewise continuous symbols on a union of a finite and semi-infinite interval. Appl. Anal., 64, 171--187, 1997.
  • D. Elliott, I. K. Lifanov, and G.S. Litvinchuk. The solution in a class of singular functions of Cauchy type bisingular integral equations. J. Integral Equations Appl., 9(3), 237--251, 1997.
  • A. B. Lebre, A. Moura Santos, and F.-O. Speck. Factorization of a class of matrices generated by Sommerfeld diffraction problems with oblique derivatives. Math. Methods Appl. Sci., 20, 1185--1198, 1997.
  • A. Moura Santos and F.-O. Speck. Sommerfeld diffraction problems with oblique derivatives. Math. Methods Appl. Sci., 20, 635--652, 1997.
  • S. Roch, P. A. Santos, and B. Silbermann. Finite section method in some algebras of multiplication and convolution operators and a flip. Z. Anal. Anwendungen, 16(3), 575--606, 1997.
  • 1996
    • A. V. Avizenshtat, Yu. I. Karlovich, and G. S Litvinchuk. The method of conformal gluing for the Haseman boundary value problem on an open contour. Complex Variables Theory Appl., 28, 313--346, 1996.
    • A. A. Baturev, V. G. Kravchenko, and G. S Litvinchuk. An approach to the approximate solution of singular integral equations with a non-Carleman shift. Dokl. Math., 53(2), 230--232, 1996.
    • A. A. Baturev, V. G. Kravchenko, and G. S Litvinchuk. Approximate methods for singular integral equations with a non-Carleman shift. J. Integral Equations Appl., 8(1), 1--17, 1996.
    • L. P. Castro and F.-O. Speck. On the inversion of higher order Wiener-Hopf operators. J. Integral Equations Appl., 8, 269--285, 1996.
    • P. A. Lopes and A. F. dos Santos. A new approach to the convolution operator on a finite interval. Integral Equations Operator Theory, 26: 460--475, 1996.
    • A. Moura Santos, F.-O. Speck, and F. S. Teixeira. Compatibility conditions in some diffraction problems. In A. H. Serbest and S. R. Cloude, editors, Direct and Inverse Electromagnetic Scattering, volume 361 of Pitman Res. Notes in Math., 25--38. Addison Wesley Longman, 1996.
    • F. Penzel and F. S. Teixeira. A Wiener-Hopf approach for the scattering by a disk. Integral Equations Operator Theory, 24, 230--247, 1996.
    • F. S. Teixeira and P. A. Santos. Sommerfeld type diffraction problems with approximate boundary conditions of arbitrary order. In A. H. Serbest and S. R. Cloude, editors, Direct and Inverse Electromagnetic Scattering, volume 361 of Pitman Res. Notes in Math., 3--14. Addison Wesley Longman, 1996.


    Publications To Appear (or Submitted)
  • H.-D. Alber, R. Farwig, F.-O. Speck, Erhard Meister (1930-2001). 7 p. To appear in Math. Nachrichten.
  • M. A. Bastos, Yu. I. Karlovich, and B. Silbermann. Toeplitz operators with symbols generated by slowly oscillating and semi-almost periodic matrix functions. To appear. Proc. London Math. Soc., 40 p.
  • M. A. Bastos, A. Bravo, Yu. Karlovich, Symbol calculus and Fredholmness for algebras of convolution type operators with slowly oscillating and piecewise continuous data.To appear Math. Nachr., 25p.
  • M. A. Bastos, A. Moura Santos, A. F. dos Santos, Wave diffration by a strip grating: the two-straight line approach, accepted Math. Nachr., 24 p.
  • M. A. Bastos, C.A. Fernandes, Yu. Karlovich, C* algebras of integral operators with piecewise slowly oscillating coefficients and shifts acting freely, 48p, submitted.
  • M.C. Câmara and M.T. Malheiro. Wiener-Hopf factorization for n x n Daniele-Khrapkov class: associate boundary-value problems on a Riemann surface and structure of the factors. Preprint DM 33/02. Submitted.
  • M.C. Câmara, S. Naique and A. F. dos Santos. Oscillatory Riemann-Hilbert problems with triangular symbols - polynomial almost periodic solutions, 2004 (submitted).
  • L. Castro and F.-O. Speck, Inversion of matrix convolution type operators with symmetry. 24 p., submitted.
  • L.P.Castro and A.Moura Santos: An operator approach for an oblique derivative boundary-transmission problem. (accepted for publication in Math. Meth. Appl. Sci. 2004)
  •  L.. Castro, R. Duduchava, and F.-O. Speck. Finite interval convolution operators with transmition property. Prep. 1/2003,15 p.
  • L. Castro, F.-O. Speck and F.S. Teixeira, A direct approach to convolution type operators with symmetry. Prep. 11/2003,18 p. To appear in Math. Nachrichten.
  • A. Karlovich and A. Lerner, Commutators of singular integrals on generalized Lp spaces with variable exponent.
  • A. Karlovich. Singular integral operators with flip and unbounded coefficients on rearrangement-invariant spaces, Departamento de Matematica, Instituto Superior Tecnico, Preprint 26/2002, 10p.
  • A. Karlovich, Singular integral operators with flip and unbounded coefficients on rearrangement-invariant spaces. Prooceedings of the International Conference on Functional Analysis and its Applications. Dedicated to the 110th anniversary of Stefan Banach, Ukraine, Lviv, May, 2002, to appear.Departamento de Matemática,  Instituto Superior Técnico, Preprint 26/2002.
  • A. Karlovich and P. Santos, On asymptotics of Toeplitz determinants with symbols of nonstandard smoothness. Departamento de Matemática,  Instituto Superior Técnico, Preprint 15/2003.
  • A. Karlovich. Norms of Toeplitz and Hankel operators on Hardy type subspaces of rearrangement-invariant spaces with Muckenhoupt weights. Integral Equations Operator Theory. To appear.
  • A. Karlovich and P.A Santos.On asymptotics of Toeplitz determinants with symbols of nonstandard smoothness. Preprint 15/2003, Departamento de Matemática do Instituto Superior Técnico.
  • Yu. Karlovich and L. Pessoa, Algebras generated by the Bergman and anti-Bergman projections and by the multiplication operators by piecewise continuous functions 55p, submited.
  • H. Mascarenhas and B. Silbermann.  Convolution type operators on cones and their finite sections. To appear Math. Nachr.
  • L. Oliveira. On the structure of inner ideals of nest algebras. Preprint DM 2/02. Submitted.
  • L. Oliveira. Weak*-closed Jordan ideals of nest algebras. Preprint DM 3/02. Math. Nachr. To appear.


  • PhD Theses
  • H. Mascarenhas. Convolution type operators on cones and asymptotic spectral theory.  PhD thesis, Technischen Universität Chemnitz,  2004. Supervisor: B. Silbermann.
  • A. Bravo. Operadores de Tipo Convolução com Símbolos Matriciais Fracamente Oscilantes e Semi-quase Periódicos PhD thesis, Instituto Superior Técnico, 2003. Supervisor: M. Amélia Bastos.
  • P. Lopes. An Invertibility Study of the Finite Interval Convolution Operator. PhD thesis, Instituto Superior Técnico, 2000. Supervisor: A. F. dos Santos.
  • A. Moura Santos. Minimal Normalization of Wiener-Hopf Operators and Applications to Sommerfeld Diffraction Problems. PhD thesis, Instituto Superior Técnico, 1999. Supervisor: F.-O. Speck.
  • L. P. Castro. Relations between Singular Operators and Applications. PhD thesis, Instituto Superior Técnico, 1998. Supervisor: F.-O. Speck.
  • P. A. Santos. Approximation Methods for Convolution Operators on the Real Line. PhD thesis, Technischen Universität Chemnitz, May 1998. Supervisor: B. Silbermann.


  • Master Theses
  • C. Diogo. Problemas de Riemann-Hilbert com símbolos triangulares oscilatórios e factorização generalizada. Master's thesis, Instituto Superior Técnico, 2004. Supervisor: M. C. Câmara.
  • N. M. Martins. A Transformação Indice. Aplicação a Operadores de Toeplitz. Master's thesis, Instituto Superior Técnico, 2002. Supervisor: M.A. Bastos.
  • C. Gavinhos. Factorização Meromorfa e Generalizada numa Álgebra de Funcões Matriciais 2x2. Master's thesis, Instituto Superior Técnico, 2002. Supervisor: M. C. Camara.
  • L. Pessoa. Espaços de Bergman e operadores de Toeplitz em espaços de Bergman. Master's thesis, Instituto Superior Técnico, 2001. Supervisor: M. A. Bastos.
  • C. Fernandes. Método de localização em órbitas - operadores com deslocamento. Master's thesis, Instituto Superior Técnico, 2000. Supervisor: M. A. Bastos.
  • P. Duarte. Um símbolo para uma álgebra de operadores num espaço com peso de Muckenhoupt. Master's thesis, Instituto Superior Técnico, 2000. Supervisor: M. A. Bastos.
  • T. Monteiro. Factorização em álgebras de funções contínuas e sistemas integráveis. Master's thesis, Instituto Superior Técnico, 2000. Supervisors: M. A. Bastos and A. F. dos Santos.
  • C. Carvalho. Álgebras localmente convexas. Master's thesis, Instituto Superior Técnico, 1999. Supervisor: F. S. Teixeira.
  • T. Malheiro. Factorização generalizada de uma classe de símbolos matriciais. Master's thesis, Instituto Superior Técnico, 1999. Supervisor: M. C. Câmara.
  • A. Conceição. Factorização de funções matriciais e o resolvente de certos operadores. Master's thesis, Instituto Superior Técnico, 1999. Supervisors: V. G. Kravchenko and F. S. Teixeira.
  • N. F. António. Álgebras C* de rotação: Propriedades elementares e de estrutura. Master's thesis, Instituto Superior Técnico, 1999. Supervisor: A. F. dos Santos.
  • H. Mascarenhas. Teoria de Gelfand generalizada. Álgebras geradas por operadores de Toeplitz e Hankel. Master's thesis, Instituto Superior Técnico, 1999. Supervisor: M. A. Bastos.
  • L. M. Cotrim. Factorização de símbolos e difracção por estruturas periódicas abertas. Master's thesis, Instituto Superior Técnico, 1998. Supervisor: M. A. Bastos.
  • R. G. Bernardino. Factorização numa álgebra. Master's thesis, Instituto Superior Técnico, 1997. Supervisor: M. C. Câmara.
  • J. M. Salazar. Símbolos de invertibilidade em álgebras de Banach. Master's thesis, Instituto Superior Técnico, 1997. Supervisor: M. C. Câmara.
  • A. Bravo. Operadores de Toeplitz e factorização de funções quase periódicas. Master's thesis, Instituto Superior Técnico, 1996. Supervisor: M. A. Bastos


  • Scientific Events
    (organized or co-organized by members of the centre)
      Operator Theory in Analysis and Engineering, Workshop in Honour of Prof. Dr. Erhard Meister, 
      Darmstadt, Germany, June 2003.  Organizers: H.-D. Alber, R. Farwig (TU Darmstadt), F.-O. Speck 
      (Lisboa). Proceedings to be published in the journal Mathematische Nachrichten.

      International Conference on Factorization, Singular Operators and Related Topics, FSORP-Madeira 2002, in honour of Georgii Litvinchuk (member of the group) to celebrate his 70th Birthday;
      University of Madeira, January 28 - February 1, 2002.
      S. Samko (chairman of the organizing committee), V. Kravchenko, A.F. dos Santos, F.S. Teixeira, A.B. Lebre, A.M. Santos (co-organizers) Proceedings published by Kluwer Academic Publishers.

      IWOTA-Portugal 2000, University of Algarve, September 12-15, 2000.
      A.F. dos Santos (chairman of the organizing committee), F.-O. Speck, A.B. Lebre, R. Picken, V. Kravchenko and N. Manojlovic (co-organizers).
      Proceedings in the series "Operator Theory: Advances and Applications", vol. 142, published by Birkhäuser.

      Summer School on Factorization and Integrable Systems, University of Algarve, September 6-9, 2000.
      A.F. dos Santos and N. Manojlovic (co-organizers).
      Lectures with the title "Factorization and Integrable Systems" in the series "Operator Theory: Advances and Applications", vol. 141, published by Birkhäuser.



    Long Term Visitors
    • Yuri Karlovich (Universidad Autónoma del Estado de Morelos, Mexico) October 1999, January and June 2000, March 2001, from October to November 2001
    • Bernd Silbermann (Technische Universität Chemnitz, Germany) September 1997, from March to September 2000, November 2001
    • Torsten Ehrhardt (Technische Universität Chemnitz, Germany) December 1996, from February to March 1998, from July to August 2001
    • Roland Duduchava (A. Razmadze Mathematical Institute, Academy of Sciences, Tbilisi, Georgia) from June to July 2000, from May to July 2001
    • Ilya Spitkovsky (College of William and Mary, Williamsburg, Virginia, USA) May 1997 and June 2001
    • N. K. Karapetiants (Rostov State University, Rostov-on-Don, Russia) from June to July 1997, May to July and October to November 1998, January to July 1999 and from September 1999 to July 2000
    • Ernst Lüneburg (Deutsche Forschungsanstalt für Luft-und Raumfahrt, Oberpfaffenhofen, Germany) July 1998
    • Frank Penzel (Technische Universität Darmstadt, Germany) from January to June 1998
    • Vladimir Rabinovich (Rostov State University, Rostov-on-Don, Russia) October 1997
    • Naum Krupnik (Bar-Ilan University, Israel) April 1997
    • Nikolai Vasilevski(University of Odessa and CINVESTAV - I.P.N., Mexico) June 1996

    Research Projects


  • Algebras of Operators of Non Local Type and Factorization of Oscillatory Symbols, IST/UTL. 

  • Funded by FCT/FEDER/POCTI
    Coordinator: M. Amélia Bastos - 


  • Operator Factorization and Applications to Mathematical Physics, IST/UTL. 

  • Funded by FCT/FEDER/PRAXIS
    Coordinator: António Ferreira dos Santos
     
  • Spline Methods for Wiener-Hopf Equations, IST/UTL in collaboration with TU Chemnitz, Germany. 

  • Funded by JNICT/BMFT (Ministry of Research and Technology, Germany
    Coordinator: Frank-Olme Speck 
     
  • Singular Operators - New Features and Applications, IST/UTL in collaboration with TU Chemnitz, Germany. 

  • Funded by JNICT/BMFT (Ministry of Research and Technology, Germany
    Coordinator: Frank-Olme Speck