Frank-Olme Speck

Professor Catedrático Convidado (retired)

Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa

Member of Deutsche Mathematiker-Vereinigung, European Mathematical Society, Sociedade Portuguesa de Matemática, the Center for Functional Analysis and Applications - CEAF, Advisory Board of Mathematische Nachrichten, Editorial Board of Integral Equations and Operator Theory, Operator Theory: Advances and Applications, Supervisory Board of Deutscher Verein in Lissabon.

Phone: +351-21 8417095
Secr CEAF: +351-21 8417084
Secr DM: +351-21 8417211
Fax: +351-21 8417598
Email: fspeck [at] math.ist.utl.pt

Postal Address:
Departamento de Matemática
Instituto Superior Técnico
Av. Rovisco Pais
1049-001 Lisboa, Portugal

Current Research Interests

Operator relations, invariance and transfer properties, and applications to particular classes of operators

New features in mixed boundary value problems: localization, normalization, compatibility conditions etc.

Singular integral and pseudodifferential equations in various functional spaces on curves with corners and cusps

Diffraction problems in conical and in canonical domains

Factorization of non-rational matrix functions, transform techniques, invariants

Non-linear Riemann boundary value problems

Convolution type operators with symmetry

Seminars, Conferences and Further Links

Seminar on Functional Analysis and Applications, current research seminar of the Operator Theory group at IST

The Functional Analysis Working Group Seminar of the Mathematics Department at Universidade de Aveiro

Seminar on Harmonic Analysis, Operator Theory and Applications of the Mathematics Department of Universidade do Algarve at Faro

Colloquium of the Mathematics Department at IST

International SimTech Symposium "Partial Differential Equations: Theory, Applications, Simulations" dedicated to Prof. Dr. Dr.h.c. Wolfgang L. Wendland on the occasion of his 75th birtday, 6-8 October 2011 at Stuttgart, Germany.

II International Conference of the Georgian Mathematical Union , 15-19 September 2011 at Batumi, Georgia.

Muskhelishvili 120, International Conference "Continuum Mechanics and Related Problems of Analysis", to celebrate the 70th Anniversary of the Georgian National Academy of Sciences and the 120th birtday of its First President Academician Nikoloz (Niko) Muskhelishvili, 9-14 September 2011 at Tbilisi, Georgia.

IWOTA 2011, The XXIIth International Workshop on Operator Theory and Applications, 3-9 July 2011 at the University of Sevilla, Spain.

IDOTA 2011, International Conference on Integral and Differential Operators and Their Applications, dedicated to Stefan Samko on the occasion of his 70th birthday. 30 June - 2 July 2011 at University of Aveiro, Portugal (to be announced soon).

STOP 2011, Summer School and Workshop on Selected Topics of Operator Theory, 23-29 June 2011 at Instituto Superior Técnico, Universidade Técnica de Lisboa, Portugal (to be announced soon).

IWOTA 2010, The XXIth International Workshop on Operator Theory and Applications, 12-16 July 2010 at Technische Universität Berlin, Germany.

Advanced School on Integral Equations , 6-8 April 2010 at Instituto Superior Técnico, Universidade Técnica de Lisboa.

Workshop on Advances and Trends in Integral Equations, dedicated to the memory of Siegfried Prößdorf. 5-9 October 2009 at Hotel Wasserschloss nearby Chemnitz, Germany.

Operator Algebras and Applications, International Summer School, 15-19 June 2009 at Instituto Superior Técnico, UT Lisboa.

IWOTA 2009, The XXth International Workshop on Operator Theory and Applications, 25-29 May 2009 at CIMAT (Center for Research in Mathematics), Guanajuato, Mexico.

II Iberian Mathematical Meeting, 3-5 October 2008 at Badajoz, Spain.

IWOTA 2008, The XIXth International Workshop on Operator Theory and Applications, 22-26 July 2008 at Williamsburg, Virginia, USA.

Analysis, PDEs and Applications, Conference on the occasion of the 70th birthday of Vladimir Maz'ya, 30 June - 3 July 2008, Rome, Italy.

BETA 2007, Boundary Elements - Theory and Applications, dedicated to Ernst Stephan on the occasion of his 60th birthday, 22-24 May 2007 at Hanover, Germany.

MAA 2007, International Conference on Modern Analysis and Applications, dedicated to the centenary of Mark Krein, 9-14 April 2007 at Odessa, Ukraine.

ICMP 2006, International Conference on Multifield Problems, 4-7 October 2006 at Stuttgart, Germany.

EWS´2006, IV. International Workshop on Electromagnetic Wave Scattering, 18-22 September 2006 at Gebze, Turkey.

AMADE 2006, Fourth International Conference on Analytic Methods of Analysis and Differential Equations, dedicated to the centenary of Fedor Dmitrievich Gakhov, 12-20 September 2006 at Minsk, Belarus.

WOAT 2006, International Summer School and Workshop on Operator Algebras, Operator Theory and Applications, 1-5 September 2006 at Lisbon, Portugal. Proceedings to appear in spring 2008, see below.

ISAAC 2005, 5th Congress of The International Society for Analysis, its Applications and Computation, 25-30 July 2005 at Catania, Italy.

OTFUSA 2005, Conference on Operator Theory, Function Spaces and Applications, 7-9 July 2005 at Aveiro, Portugal. Proceedings in Math. Nachrichten 280 (2007), Special Issue 9-10, edited by L.P. Castro.

Research Report 2009 of the Center for Functional Analysis and Applications

Research Report 2008 of the Center for Functional Analysis and Applications

Projects

Operator Theoretical Methods in Problems of Diffraction by Wedges and Cones. FCT project SFRH/BPD/38273/2007, 2007-10, jointly with A.P. Nolasco, Aveiro, Portugal.

Toeplitz Operators, Factorization and Corona Problems. I&D project 2007-09, coordinated by M.C. Câmara.

Operator Theoretical Methods in Boundary Value Problems. CEMAT project 2003-06, jointly with F.S. Teixeira, continued in CEAF 2006-09.

Algebras of Operators of Non-local Type and Factorization of Oscillatory Symbols. PRAXIS XXI project 1999-2001, coordinated by A. Bastos.

Normalization of Operators. CMA project 1997-2002.

Operator Factorization and Applications to Mathematical Physics. PRAXIS XXI project 1996-2002, coordinated by A. F. dos Santos.

Spline Methods for Wiener-Hopf Equations. JNICT/BMFT project 423/2, 1995-1999, jointly with B. Silbermann, TU Chemnitz, Germany.

Singular Operators - New Features and Applications. JNICT/BMFT project 423/1, 1995-1998, jointly with E. Meister, TU Darmstadt, Germany.

Recent and Selected Publications

Diffraction by a three-quarter-plane using an abstract Babinet principle. Submitted, 7p.

On the reduction of linear systems related to boundary value problems. Submitted, 16 p.

Boundary integral methods for wedge diffraction problems: the angle 2 pi/n, Dirichlet and Neumann conditions (with T. Ehrhardt and A.P. Nolasco). Operators and Matrices 5 (2011), 1-40.

On the weak solution of the Neumann problem for the 2D Helmholtz equation in a convex cone and H^sregularity (with A.E. Merzon and T.J. Villalba-Vega). Math. Meth. Appl. Sci. 34 (2011), 24-43. DOI 10.1002/mma.1326

On the analytical solution of the linear-fractional Riemann problem (with S. Rogosin). Math. Nachrichten 284 (2011), 543-559. DOI 10.1002/mana.200810133

Boundary value problems for the Helmholtz equation in an octant (with E.P. Stephan). Integr. Equ. Oper. Theory 62 (2008), 269-300.

Operator Algebras, Operator Theory and Applications (with M.A. Bastos, I. Gohberg and A.B. Lebre). Proceedings of an International Summer School and Workshop “WOAT 2006” held at Lisbon in September 2006. Operator Theory: Advances and Applications, vol. 181, Birkhäuser, Basel 2008, xiv + 437 p.

Solvability of singular integro-differential equations with multiple complex shifts (with L. Castro and R. Duduchava). Complex Analysis and Operator Theory (special issue devoted to the memory of Georgii Semenovich Litvinchuk, editors D. Alpay, M. Shapiro and I. Spitkovsky), 16 p, online publication DOI 10.1007/s11785-008-0055-0 (2008).

Asymmetric factorizations of matrix functions on the real line (with L.P. Castro and R. Duduchava). In: Modern Operator Theory and Applications. The Igor Borisovich Simonenko Anniversary Volume (eds. Y.M. Erusalimskii et al), Operator Theory: Advances and Applications, vol. 170, Birkhäuser, Basel 2006, 53-74.

Mixed boundary value problems for the Helmholtz equation in a quadrant (with L. Castro and F.S. Teixeira). Integr. Equ. Oper. Theory 56 (2006), 1-44. Online publ. DOI 10.1007/s00020-005-1410-4 (2005).

Inversion of matrix convolution type operators with symmetry (with L. Castro). Portugaliae Mathematica 62 (2005), 193-216.

Finite interval convolution operators with transmission property (with L. Castro and R. Duduchava). Integr. Equ. Oper. Theory 52 (2005), 165-179.

In Honour of Erhard Meister (Laudatio, with H.-D. Alber and R. Farwig). Math. Nachrichten 269-270 (2004), 4-10.

Operator Theoretical Methods and Applications to Mathematical Physics. The Erhard Meister Memorial Volume (with I. Gohberg, A.F. dos Santos, F.S. Teixeira, W. Wendland). Operator Theory: Advances and Applications, Vol. 147, Birkhäuser, Basel 2004, xvi + 476 p.

In Memory of Erhard Meister (a short biography). In: Operator Theoretical Methods and Applications to Mathematical Physics (Eds. I. Gohberg et al.). Operator Theory: Advances and Applications, Vol. 147, Birkhäuser, Basel 2004, 27-46.

A direct approach to convolution type operators with symmetry (with L. Castro and F.S. Teixeira). Math. Nachrichten 269-270 (2004), 73-85.

On a class of wedge diffraction problems posted by Erhard Meister (with L. Castro and F.S. Teixeira). In: Operator Theoretical Methods and Applications to Mathematical Physics (Eds. I. Gohberg et al.). Operator Theory: Advances and Applications, Birkhäuser, Basel 2004, 211-238.

Explicit solution of a Dirichlet-Neumann wedge diffraction problem with a strip (with L. Castro and F.S. Teixeira). Journal of Integral Equations and Applications (2003), 359-383.

Well-posedness of diffraction problems involving a coplanar strip (with L. Castro). In: Singular Integral Operators, Factorization and Applications, Proceedings IWOTA-Portugal 2000, Operator Theory: Advances and Applications, Vol. 142, Birkhäuser, Basel 2003, 81-93.

Singular Integral Operators, Factorization and Applications (with A. Böttcher, M.A. Kaashoek, A. Lebre and A.F. dos Santos). Proceedings IWOTA-Portugal 2000, Operator Theory: Advances and Applications, Vol. 142, Birkhäuser, Basel 2003, 404 p.

In memoriam Professor Erhard Meister (1930-2001). Math. Methods Appl. Sci. 25 (2002) 1-2.

Localization and minimal normalization of some basic mixed boundary value problems (with L. Castro and R. Duduchava). In: Factorization, Singular Operators and Related Problems, Proceedings of the Conference in Honour of Professor Georgii Litvinchuk at Funchal, Portugal 2002 (Eds. S. Samko et al.), Kluwer, Dordrecht 2003, 73-100.

Singular integral equations on piecewise smooth curves in spaces of smooth functions (with L. Castro and R. Duduchava). In: Toeplitz Matrices, Convolution Operators, and Integral Equations (Eds. A. Böttcher et alt.), Operator Theory: Advances and Applications, Vol. 135, Birkhäuser, Basel 2002, 107-144.

Transformation techniques towards the factorization of non-rational 2 x 2 matrix functions (with T. Ehrhardt). Linear Algebra and its Applications 353 (2002) 53-90.

Relations between convolution type operators on intervals and on the half-line (with L. Castro). Integr. Equat. Oper. Th. 37 (2000), 169-207.

Regularity properties and generalized inverses of delta-related operators (with L. Castro). Zeitschr. Anal. Anw. 17 (1998), 577-598.

Minimal normalization of Wiener-Hopf operators in spaces of Bessel potentials (with A. Moura Santos e F. S. Teixeira). J. Math. Anal. Appl. 225 (1998), 501-531.

Compatibility conditions in some diffraction problems (with A. Moura Santos e F. S. Teixeira). In: Proc. Conf. Gebze, Istanbul 1995. Pitman Research Notes in Mathematics Series 361. Longman, London 1996, 25-38.

Generalised factorisation for a class of Jones form matrix functions (with M. C. Câmara e A. B. Lebre). Proc. Royal Soc. Edinburgh 123 A (1993), 401-422.

Some interior and exterior boundary value problems for the Helmholtz equation in a quadrant (with E. Meister, F. Penzel e F. S. Teixeira). Proc. Royal Soc. Edinburgh 123 A (1993), 275-294.

Pseudodifferential operators on compact manifolds with Lipschitz boundary (with R. Duduchava). Math. Nachr. 160 (1993), 149-191.

Meromorphic factorization, partial index estimates and elastodynamic diffraction problems (with M. C. Câmara e A. B. Lebre). Math. Nachr. 157 (1992), 291-317.

Bessel potential operators for the quarter-plane (with R. Duduchava). Appl. Anal. 45 (1992), 49-68.

A factorization procedure for two by two matrix functions on the circle with two rationally independent entries (with S. Prössdorf). Proc. Royal Soc. Edinburgh 115 A (1990), 119-138.

The explicit solution of elastodynamical diffraction problems by symbol factorization (com E. Meister). Z. Anal. Anw. 8 (1989), 307-328.

Modern Wiener-Hopf methods in diffraction theory (with E. Meister). In: Ordinary and Partial Differential Equations, Vol. 2 (Ed. B. D. Sleeman, R. J. Jarvis). Proc. Conf. Dundee (Scotland) 1988. Longman, London 1989, 130-171.

Sommerfeld diffraction problems with third kind boundary conditions (with R. A. Hurd e E. Meister). SIAM J. Math. Anal. 20 (1989), 589-607.

Sommerfeld diffraction problems with first and second kind boundary conditions. SIAM J. Math. Anal. 20 (1989), 396-407.

Mixed boundary value problems of the type of Sommerfeld's half-plane problem. Proc. Royal Soc. Edinburgh 104 A (1986), 261-277.

General Wiener-Hopf Factorization Methods. Research Notes in Mathematics 119. Pitman, London 1985, 157p.

Some multi-dimensional Wiener-Hopf equations with applications (with E. Meister). In: Trends in Applications of Pure Mathematics to Mechanics II (Ed. H. Zorski). Proc. Conf. Kozubnik (Poland) 1977. Pitman, London 1979, 217-262.