This webpage is devoted to my academic activities. The main aim is to provide basic information about me and to share sources with scientific content.
About me
My name is František Štampach and currently I am an Assistant Professor at Department of Mathematics of the Faculty of Nuclear Sciences and Physical Engineering at Czech Technical University in Prague, and member of the MAFIA group.
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My Curiculum Vitae (not updated) and my Doctoral Thesis.
Preprints
- A. Pushnitski, F. Štampach, A functional model and tridiagonalisation for symmetric anti-linear operators, preprint [arXiv].
- M. Jex, F. Štampach, On the ground state of lattice Schrödinger operators, preprint [arXiv].
- B. Gerhat, D. Krejčiřík, F. Štampach, Criticality transition for positive powers of the discrete Laplacian on the half line, preprint [arXiv].
Articles in journals
- B. Gerhat, D. Krejčiřík, F. Štampach, An improved discrete Rellich inequality on the half-line, to appear in Israel J. Math. (2024) [arXiv].
- A. Pushnitski, F. Štampach, An inverse spectral problem for non-self-adjoint Jacobi matrices, Int. Math. Res. Not. 2024 (2024) 6106-6139 [arXiv, doi].
- P. Blaschke, F. Štampach, Asymptotic root distribution of Charlier polynomials with large negative parameter, J. Math. Anal. Appl. 524 (2023) 1-29 [arXiv, doi].
- F. Štampach, Asymptotic spectral properties of the Hilbert L-matrix, SIAM J. Matrix Anal. Appl. 43 (2022) 1658-1679 [arXiv, doi].
- D. Krejčiřík, A. Laptev, F. Štampach, Spectral enclosures and stability for non-self-adjoint discrete Schrödinger operators on the half-line, Bull. London Math. Soc. 54 (2022) 2379-2403 [arXiv, doi].
- F. Štampach, The Hilbert L-matrix, J. Funct. Anal. 282 (2022) 1-46 [arXiv, doi].
- D. Krejčiřík, F. Štampach, A sharp form of the discrete Hardy inequality and the Keller-Pinchover-Pogorzelski inequality, Amer. Math. Monthly. 129 (2022) 281-283 [arXiv, doi].
- S. Bögli, F. Štampach, On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators, J. Spectr. Theory 11 (2021) 1391-1413 [arXiv, doi].
- F. Štampach, P. Šťovíček, New explicitly diagonalizable Hankel matrices related to the Stieltjes-Carlitz polynomials, Integr. Equ. Oper. Theory 93 (2021) 1-39 [arXiv, doi].
- F. Štampach, Asymptotic behaviour and zeros of the Bernoulli polynomials of the second kind, J. Approx. Theory 262, (2021) 1-28 [arXiv, doi].
- T. Kalvoda, F. Štampach, New family of symmetric orthogonal polynomials and a solvable model of a kinetic spin chain, J. Math. Phys. 61 (2020) 1-21 [arXiv, doi]].
- B. Cassano, O. O. Ibrogimov, D. Krejčiřík, F. Štampach, Location of eigenvalues of non-self-adjoint discrete Dirac operators, Ann. Henri Poincaré 21 (2020) 2193-2217 [arXiv, doi].
- P. Blaschke, F. Štampach, The asymptotic zero distribution of Lommel polynomials as polynomials of their order with a variable complex argument, J. Math. Anal. Appl. 490 (2020) 1-19 [arXiv, doi].
- F. Štampach, P. Šťovíček, On Hankel matrices commuting with Jacobi matrices from the Askey scheme, Linear Alg. Appl. 591 (2020) 235-267 [arXiv, doi].
- O. O. Ibrogimov, F. Štampach, Spectral enclosures for non-self-adjoint discrete Schrödinger operators, Integr. Equ. Oper. Theory 91 (2019) 1-15 [arXiv, doi].
- M. E. H. Ismail, F. Štampach, Spectral analysis of two doubly infinite Jacobi matrices with exponential entries, J. Funct. Anal. 276 (2019) 1681-1716 [arXiv, doi].
- F. Štampach, P. Šťovíček, Spectral representation of some weighted Hankel matrices and orthogonal polynomials from the Askey scheme, J. Math. Anal. Appl. 472 (2019) 483-509 [arXiv, doi].
- B. Shapiro, F. Štampach, Non-self-adjoint Toeplitz matrices whose principal submatrices have real spectrum, Constr. Approx. 49 (2019) 191-226 [arXiv, doi]; Correction: Non-Self-Adjoint Toeplitz Matrices Whose Principal Submatrices Have Real Spectrum, Constr. Approx. (2023) [doi].
- Á. Baricz, F. Štampach, The Hurwitz-type theorem for the regular Coulomb wave function via Hankel determinants, Linear Alg. Appl. 548 (2018) 259-272 [arXiv, doi].
- P. Siegl, F. Štampach, Spectral analysis of non-self-adjoint Jacobi operator associated with Jacobian elliptic functions, Oper. Matrices 11 (2017) 901-928 [arXiv, doi].
- F. Štampach, The characteristic function for complex doubly infinite Jacobi matrices, Integr. Equ. Oper. Theory 88 (2017) 501-534 [arXiv, doi].
- F. Štampach, P. Šťovíček, Factorization of the characteristic function of a Jacobi matrix, Oper. Matrices 11 (2017) 147-169 [arXiv, doi].
- P. Siegl, F. Štampach, On extremal properties of Jacobian elliptic functions with complex modulus, J. Math. Anal. Appl. 442 (2016) 627-641 [arXiv, doi].
- F. Štampach, Nevanlinna extremal measures for polynomials related to q-1-Fibonacci polynomials, Adv. Appl. Math. 78 (2016) 56-75 [arXiv, doi].
- F. Štampach, P. Šťovíček, The Nevanlinna parametrization for q-Lommel polynomials in the indeterminate case, J. Approx. Theory 201 (2016) 48-72 [arXiv, doi].
- F. Štampach, P. Šťovíček, Special functions and spectrum of Jacobi matrices, Linear Alg. Appl. 464 (2015) 38-61 [arXiv, doi].
- F. Štampach, P. Šťovíček, The Hahn-Exton q-Bessel function as the characteristic function of a Jacobi matrix, Spec. Matrices 2 (2014) 131-147 [arXiv, doi].
- F. Štampach, P. Šťovíček, Orthogonal polynomials associated with Coulomb wave functions, J. Math. Anal. Appl. 419 (2014) 231-254 [arXiv, doi].
- F. Štampach, P. Šťovíček, The characteristic function for Jacobi matrices with applications, Linear Alg. Appl. 438 (2013) 4130-4155 [arXiv, doi].
- F. Štampach, P. Šťovíček, On the Eigenvalue Problem for a Particular Class of Finite Jacobi Matrices, Linear Alg. Appl. 434 (2011) 1336-1353 [arXiv, doi].
Book chapter
- F. Štampach, P. Šťovíček, On diagonalizable quantum weighted Hankel matrices, Toeplitz Operators and Random Matrices: In Memory of Harold Widom, Operator Theory: Advances and Applications, 289, Birkhäuser, 2022 [arXiv, doi].
Current grant projects
- 2020-2024: GAČR EXPRO grant No. 20-17749X "New challenges for spectral theory: geometry, artificial materials and complex fields" (member); see the webpage devoted to project activities.
Talks
Here is a list of several talks I gave.
- November 2023, London, Orthogonal Polynomials, Special Functions, Operator Theory and Applications
talk: An inverse spectral problem for non-self-adjoint Jacobi matrices [talk] - July 2023, Évora, Workshop on Operator Theory, Complex Analysis, and Applications
talk: Inverse spectral problem for non-self-adjoint Jacobi matrices [slides] - January 2023, Stockholm, Analysis group seminar at Stockholm University
talk: On discrete Hardy inequalities [slides] - July 2022, Banff, Mathematical aspects of the Physics with non-self-Adjoint Operators
talk: An open problem on the discrete Rellich inequality [slides] - June 2022, Faro, Workshop on Operator Theory, Complex Analysis, and Applications
talk: An improved discrete Rellich inequality [slides] - April 2022, London, London Analysis and Probability seminar at King's College London
talk: Spectrum of the Hilbert L-matrix [slides] - February 2022, Durham, Analysis & PDE Seminar at Durham University
(on-line) talk: Optimal spectral enclosures for 1D discrete Schrödinger operators with complex potentials [slides] - August 2021, Los Angeles, International Workshop on Operator Theory and its Applications
(on-line) talk: On the Hilbert L-matrix [slides] - June 2021, Lisbon, Workshop on Operator Theory, Complex Analysis, and Applications
talk: Spectral bounds for 1D discrete Schrödinger operators with complex potentials [slides] - February 2021, Marseille, Mathematical aspects of the physics with non-self-adjoint operators
talk: On Lieb–Thirring inequlities for non-self-adjoint Jacobi matrices and Schrödinger operators [slides] - September 2019, Sveti Martin na Muri, The 6th Najman Conference on Spectral Theory and Differential Equations
talk: Spectral bounds for 1D discrete Schrödinger and Dirac operators with complex potentials [slides] - July 2019, Lisbon, International Workshop on Operator Theory and its Applications
talk: New explicitly diagonalizable Hankel matrices [slides] - September 2018, Belfast, Colloquium for Queen’s University Belfast
talk: On the asymptotic eigenvalue distribution of generalized Toeplitz matrices [slides] - May 2018, Stockholm, Hausdorff Geometry of Polynomials and Polynomial Sequences Conference
talk: On the asymptotic zero distribution of orthogonal polynomials on the unit circle with variable
Verblunsky coefficients [slides] - February 2018, Ostrava, Seminar talk at Ostrava University
talk: On the asymptotic eigenvalue distribution of Toeplitz matrices and generalizations [slides] - September 2017, Opatija, The Fifth Najman Conference on Spectral Theory and Differential Equations
talk: On non-self-adjoint Toeplitz matrices with purely real spectrum [slides] - July 2017, Děčín, Methods of Algebra and Functional Analysis in Applications, summer school
talk: An invitation to the non-self-adjoint church [slides] - June 2017, Děčín, Symmetries of Discrete Systems and Processes
talk: Non-self-adjoint Toeplitz matrices with real spectrum and related orthogonal polynomials [slides] - June 2017, Hong Kong, International Conference on Special Functions: Theory, Computation, and Applications
talk: Non-self-adjoint Toeplitz matrices with purely real spectrum and related problems [slides] - November 2016, Stockholm, Analysis Group Seminar
talk: The moment problem [slides] - August 2016, Saint Petersburg, Operator Theory, Analysis and Mathematical Physics
talk: Spectral analysis of some doubly infinite Jacobi matrices via characteristic function [slides] - June 2016, Timisoara, The 26th International Conference in Operator Theory
talk: Spectral analysis of certain doubly infinite Jacobi matrices via characteristic function [slides] - June 2016, Coimbra, Workskop on Operator Theory, Complex Analysis, and Applications
talk: Spectral analysis of non-self-adjoint Jacobi operator associated with Jacobian elliptic functions
[slides] - March 2016, Prague, Quantum Circle Seminar
talk: On the localization of spectra of complex sampling Jacobi matrices and open problems [slides] - March 2016, Stockholm, Spectral Theory and Applications
talk: Spectral analysis of two doubly infinite Jacobi operators [slides] - October 2015, Bern, Young Researchers Workshop on Spectral Theory
talk: Spectral analysis of a complex Jacobi matrix associated with Jacobian elliptic functions [slides] - August 2015, Telč, Methods of Algebra and Functional Analysis in Applications, summer school
talk: On the Ising spin model [slides] - August 2015, Děčín, Symmetries of Discrete Systems and Processes
talk: Nevanlinna extremal measures for polynomials related to q-Fibonacci polynomials [slides] - May 2015, Kruh u Jilemnice, School on Theoretical Informatics, Graphs and Mathematics
talk: How Pusheen uses computers to do mathematics [slides] - November 2014, Kuwait City, Conference on Mathematics and Applications
talk: On certain function with applications concerning tridiagonal matrices [slides] - July 2014, Stockholm, Operator Theory, Analysis and Mathematical Physics
talk: The Nevanlinna parametrization and orthognality relations for q-Lommel polynomials in the
indeterminate case [slides] - May 2014, Kruh u Jilemnice, Combinatorics on Words and Mathematical Physics,
talk: Introduction to the Theory of Orthogonal Polynomials [slides]
- January 2014, Puerto de la Cruz, An International Symposium on Orthogonality, Quadrature and Related Topics
talk: Nevanlinna functions and orthognality relations for q-Lommel polynomials [slides] - December 2013, Bangalore, International Workshop on Operator Theory and Its Applications
talk: The characteristic function for infinite Jacobi matrices, the spectral zeta function, and solvable
examples [slides] - August 2013, Bedlewo, Formal and Analytic Solutions of Differential, Difference and Discrete Equations
talk: Constructing measures of orthogonality with applications [slides] - May 2013, Dolní Lomná, Combinatorics on Words and Mathematical Physics,
talk 1: One-parameter Generalization of Some Classes of Orthogonal Polynomials [slides]
talk 2: Continued Fractions Appearing Naturally in Spectral Analysis of Jacobi Operators [slides] - May 2013, Řež u Prahy, Seminar at Nuclear Physics Institute ASCR
talk: Moment Problem [slides] - November 2012, Wroclaw, Seminar at Institute of Theoretical Physics, University of Wroclaw
talk: Spectral Analysis of Jacobi Operators and Related Problems [slides] - June 2012, Barcelona, Operator Theory, Analysis and Mathematical Physics Conference
talk: Recent Progress on Spectral Analysis of Jacobi Matrices and Related Problems [slides] - May 2012, Svatý Ján pod Skalou, Combinatorics on Words and Mathematical Physics
talk: The Characteristic Function for Jacobi Matrices with Applications [slides] - July 2011, Sevilla, 22nd International Workshop on Operator Theory and its Applications
talk: On the Eigenvalue Problem for a Certain Class of Jacobi Matrices [slides] - May 2011, Fryšava, Combinatorics on Words and Mathematical Physics
talk: On Function F and the Eigenvalue Problem for a Certain Class of Jacobi Matrices [slides] - February 2011, Bressanone, Fourth School and Workshop on "Mathematical Methods in Quantum Mechanics"
talk: On the Eigenvalue Problem for a Certain Class of Infinite Jacobi Matrices [slides] - September 2010, Hradec Králové, QMath11 Mathematical Results in Quantum Physics
talk: On the Eigenvalue Problem for a Particular Class of Jacobi Matrices [slides]
Organized meetings
- December 19-22, 2022, Graz, Workshop: Challenges in Spectral Theory of Differential Operators.
Journals refereed for
- Advances in Mathematical Physics
- Analysis and Applications
- Analysis and Mathematica Physics
- Analysis Mathematica
- Applied Mathematics and Computation
- Computational and Applied Mathematics
- Constructive Approximations
- Documenta Mathematica
- Integral Equations and Operator Theory
- Inverse Problems in Science and Engineering
- Journal of Difference Equations and Applications
- Journal of Mathematical Analysis and Applications
- Linear Algebra and its Applications
- Methods of Functional Analysis and Topology
- Mathematical Reviews, American Mathematical Society
- Numerical Algorithms
- Operators and Matrices
- Positivity
- Results in Mathematics
- Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
- The Ramanujan Journal
Useful links
- DLMF - Digital Library of Mathematical Functions
- Abramowitz and Stegun - Handbook of Mathematical Functions
- Wolfram functions site - useful while working with special functions
- Askey-scheme - comprehensive list of classical orthogonal polynomials and their q-analogues
- OEIS - The On-Line Encyclopedia of Integer Sequences
- LibGen - Library Genesis
- FAQM - Frequently Asked Questions in Mathematics