František Štampach

About me

My name is František Štampach and I am an Associate Professor at the Department of Mathematics of the Faculty of Nuclear Sciences and Physical Engineering at Czech Technical University in Prague, and a member of the MAFIA group.

Office
Czech Technical University in Prague
Faculty of Nuclear Sciences and Physical Engineering
Department of Mathematics
Trojanova 13, 120 00 Praha 2, Czech Republic
Email
stampfra@cvut.cz
Identifiers
ORCID · Scopus · MathSciNet
František Štampach

Research interests: Spectral analysis of linear operators (Jacobi, Hankel, Toeplitz, Schrödinger, etc.), mathematical methods in quantum physics, non-selfadjoint operators, orthogonal polynomials, special functions, moment problem.

My Curriculum Vitae (not updated).

Preprints05

  1. F. Štampach, J. Waclawek: Optimal Hardy weights for the fractional discrete Dirichlet Laplacian on the half-line, preprint [PDF, arXiv].
  2. F. Štampach, J. Waclawek: Optimal fractional discrete Hardy inequalities on the half-line, preprint [PDF, arXiv].
  3. F. Štampach, J. Waclawek: Optimal discrete p-Hardy-Rellich-Birman inequalities, preprint [PDF, arXiv].
  4. F. Štampach, J. Waclawek: The p-Hardy-Rellich-Birman inequalities on the half-line, preprint [PDF, arXiv].
  5. A. Pushnitski, F. Štampach: Schrödinger operators on the half-line with integrable complex potentials, preprint [PDF, arXiv].

Publications38

  1. R. Kozhan, F. Štampach: Ratio asymptotics and zero density for orthogonal polynomials with varying Verblunsky coefficients, accepted in Adv. Approx. Theor. (2026) [PDF, arXiv].
  2. A. Pushnitski, F. Štampach: The Borg-Marchenko uniqueness theorem for complex potentials, accepted in J. Math. Pures Appl. (2026) [PDF, arXiv].
  3. F. Štampach, J. Waclawek: Optimal discrete Hardy-Rellich-Birman inequalities, to appear in J. Anal. Math. (2026) 275-302 [PDF, arXiv].
  4. A. Pushnitski, F. Štampach: A functional model and tridiagonalisation for symmetric anti-linear operators, J. Operator Theory 95 (2026) 101-128 [PDF, arXiv, doi].
  5. F. Štampach, J. Waclawek: A Herglotz-Nevanlinna function from the optimal discrete p-Hardy weight, Proc. Amer. Math. Soc. 154 (2026) 807-819 [PDF, arXiv, doi].
  6. S. Bögli, S. Petpradittha, F. Štampach: On Lieb-Thirring inequalities for multidimensional Schrödinger operators with complex potentials, Integr. Equ. Oper. Theory 97 (2025) 1-34 [PDF, arXiv, doi].
  7. B. Gerhat, D. Krejčiřík, F. Štampach: Criticality transition for positive powers of the discrete Laplacian on the half line, Rev. Mat. Iberoam. 41 (2025) 1173-1200 [PDF, arXiv, doi].
  8. B. Gerhat, D. Krejčiřík, F. Štampach: An improved discrete Rellich inequality on the half-line, Israel J. Math. 268 (2025) 45-72 [PDF, arXiv, doi].
  9. M. Jex, F. Štampach: On the ground state of lattice Schrödinger operators, J. Spectr. Theory 15 (2025) 647-678 [PDF, arXiv, doi].
  10. A. Pushnitski, F. Štampach: An inverse spectral problem for non-self-adjoint Jacobi matrices, Int. Math. Res. Not. 2024 (2024) 6106-6139 [PDF, arXiv, doi].
  11. P. Blaschke, F. Štampach: Asymptotic root distribution of Charlier polynomials with large negative parameter, J. Math. Anal. Appl. 524 (2023) 1-29 [PDF, arXiv, doi].
  12. F. Štampach: Asymptotic spectral properties of the Hilbert L-matrix, SIAM J. Matrix Anal. Appl. 43 (2022) 1658-1679 [PDF, arXiv, doi].
  13. 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 [PDF, arXiv, doi].
  14. F. Štampach: The Hilbert L-matrix, J. Funct. Anal. 282 (2022) 1-46 [PDF, arXiv, doi].
  15. 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 [PDF, arXiv, doi].
  16. 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 [PDF, arXiv, doi].
  17. F. Štampach, P. Šťovíček: New explicitly diagonalizable Hankel matrices related to the Stieltjes-Carlitz polynomials, Integr. Equ. Oper. Theory 93 (2021) 1-39 [PDF, arXiv, doi].
  18. F. Štampach: Asymptotic behaviour and zeros of the Bernoulli polynomials of the second kind, J. Approx. Theory 262, (2021) 1-28 [PDF, arXiv, doi].
  19. 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 [PDF, arXiv, doi].
  20. 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 [PDF, arXiv, doi].
  21. 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 [PDF, arXiv, doi].
  22. F. Štampach, P. Šťovíček: On Hankel matrices commuting with Jacobi matrices from the Askey scheme, Linear Alg. Appl. 591 (2020) 235-267 [PDF, arXiv, doi].
  23. O. O. Ibrogimov, F. Štampach: Spectral enclosures for non-self-adjoint discrete Schrödinger operators, Integr. Equ. Oper. Theory 91 (2019) 1-15 [PDF, arXiv, doi].
  24. M. E. H. Ismail, F. Štampach: Spectral analysis of two doubly infinite Jacobi matrices with exponential entries, J. Funct. Anal. 276 (2019) 1681-1716 [PDF, arXiv, doi].
  25. 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 [PDF, arXiv, doi].
  26. B. Shapiro, F. Štampach: Non-self-adjoint Toeplitz matrices whose principal submatrices have real spectrum, Constr. Approx. 49 (2019) 191-226; Correction: Non-Self-Adjoint Toeplitz Matrices Whose Principal Submatrices Have Real Spectrum, Constr. Approx. (2023) [PDF, correction PDF, arXiv, doi, doi].
  27. Á. Baricz, F. Štampach: The Hurwitz-type theorem for the regular Coulomb wave function via Hankel determinants, Linear Alg. Appl. 548 (2018) 259-272 [PDF, arXiv, doi].
  28. P. Siegl, F. Štampach: Spectral analysis of non-self-adjoint Jacobi operator associated with Jacobian elliptic functions, Oper. Matrices 11 (2017) 901-928 [PDF, arXiv, doi].
  29. F. Štampach: The characteristic function for complex doubly infinite Jacobi matrices, Integr. Equ. Oper. Theory 88 (2017) 501-534 [PDF, arXiv, doi].
  30. F. Štampach, P. Šťovíček: Factorization of the characteristic function of a Jacobi matrix, Oper. Matrices 11 (2017) 147-169 [PDF, arXiv, doi].
  31. P. Siegl, F. Štampach: On extremal properties of Jacobian elliptic functions with complex modulus, J. Math. Anal. Appl. 442 (2016) 627-641 [PDF, arXiv, doi].
  32. F. Štampach: Nevanlinna extremal measures for polynomials related to q^-1-Fibonacci polynomials, Adv. Appl. Math. 78 (2016) 56-75 [PDF, arXiv, doi].
  33. F. Štampach, P. Šťovíček: The Nevanlinna parametrization for q-Lommel polynomials in the indeterminate case, J. Approx. Theory 201 (2016) 48-72 [PDF, arXiv, doi].
  34. F. Štampach, P. Šťovíček: Special functions and spectrum of Jacobi matrices, Linear Alg. Appl. 464 (2015) 38-61 [PDF, arXiv, doi].
  35. F. Štampach, P. Šťovíček: The Hahn-Exton q-Bessel function as the characteristic function of a Jacobi matrix, Spec. Matrices 2 (2014) 131-147 [PDF, arXiv, doi].
  36. F. Štampach, P. Šťovíček: Orthogonal polynomials associated with Coulomb wave functions, J. Math. Anal. Appl. 419 (2014) 231-254 [PDF, arXiv, doi].
  37. F. Štampach, P. Šťovíček: The characteristic function for Jacobi matrices with applications, Linear Alg. Appl. 438 (2013) 4130-4155 [PDF, arXiv, doi].
  38. F. Štampach, P. Šťovíček: On the Eigenvalue Problem for a Particular Class of Finite Jacobi Matrices, Linear Alg. Appl. 434 (2011) 1336-1353 [PDF, arXiv, doi].

Book chapter

  1. 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 [PDF, arXiv, doi].

Grant projects

  • Since 2025: No grant.
  • 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. [EXPRO, webpage]

Talks53

Here is a list of several talks I gave.

  • The New Frontier of Herglotz-Nevanlinna Functions: Theory, Applications, and Open Problems · November 2026 · Banff
    The Classical Moment Problem: An Introduction and Connections in Analysis [talk]
  • Geometric and analytic functional inequalities on discrete spaces · September 2026 · Sanya
    Optimal Hardy inequalities for powers of the discrete Laplacian on the half-line [talk]
  • Workshop on Operator Theory, Complex Analysis, and Applications · July 2026 · Guimarães
    Optimal discrete p-Hardy--Rellich--Birman inequalities [talk]
  • Mathematical aspects of the physics with non-self-adjoint operators · April 2026 · Marseille
    The spectral pair for Schrödinger operators with complex integrable potentials [talk]
  • Workshop on Operator Theory, Complex Analysis, and Applications · July 2025 · Aveiro
    The spectral pair for Schrödinger operators with complex potentials on the half-line [talk]
  • Spectral Theory and Applications in Mathematical Physics · June 2025 · Bern
    On the spectral pair for Schrödinger operators with complex potentials on the half-line [talk]
  • Mathphys Analysis Seminar at ISTA · February 2025 · Vienna
    An inverse spectral problem for non-self-adjoint Jacobi and Schrödinger operators [talk]
  • Doppler Institute Seminar · January 2025 · Prague
    An inverse spectral problem for non-self-adjoint Jacobi and Schrödinger operators [talk]
  • Workshop on Operator Theory, Complex Analysis, and Applications · July 2024 · Funchal
    A functional model and tridiagonalisation for symmetric anti-linear operators [talk]
  • Mathematical aspects of the physics with non-self-adjoint operators · June 2024 · Marseille
    A Borg-Marchenko type theorem for Schrödinger operators with complex potentials [talk]
  • Orthogonal Polynomials, Special Functions, Operator Theory and Applications · November 2023 · London
    An inverse spectral problem for non-self-adjoint Jacobi matrices [talk]
  • Workshop on Operator Theory, Complex Analysis, and Applications · July 2023 · Évora
    Inverse spectral problem for non-self-adjoint Jacobi matrices [slides]
  • Analysis group seminar at Stockholm University · January 2023 · Stockholm
    On discrete Hardy inequalities [slides]
  • Mathematical aspects of the Physics with non-self-Adjoint Operators · July 2022 · Banff
    An open problem on the discrete Rellich inequality [slides]
  • Workshop on Operator Theory, Complex Analysis, and Applications · June 2022 · Faro
    An improved discrete Rellich inequality [slides]
  • London Analysis and Probability seminar at King's College London · April 2022 · London
    Spectrum of the Hilbert L-matrix [slides]
  • Analysis & PDE Seminar at Durham University · February 2022 · Durham
    Optimal spectral enclosures for 1D discrete Schrödinger operators with complex potentials [slides]
  • International Workshop on Operator Theory and its Applications · August 2021 · Los Angeles
    On the Hilbert L-matrix [slides]
  • Workshop on Operator Theory, Complex Analysis, and Applications · June 2021 · Lisbon
    Spectral bounds for 1D discrete Schrödinger operators with complex potentials [slides]
  • Mathematical aspects of the physics with non-self-adjoint operators · February 2021 · Marseille
    On Lieb–Thirring inequalities for non-self-adjoint Jacobi matrices and Schrödinger operators [slides]
  • The 6th Najman Conference on Spectral Theory and Differential Equations · September 2019 · Sveti Martin na Muri
    Spectral bounds for 1D discrete Schrödinger and Dirac operators with complex potentials [slides]
  • International Workshop on Operator Theory and its Applications · July 2019 · Lisbon
    New explicitly diagonalizable Hankel matrices [slides]
  • Colloquium for Queen’s University Belfast · September 2018 · Belfast
    On the asymptotic eigenvalue distribution of generalized Toeplitz matrices [slides]
  • Hausdorff Geometry of Polynomials and Polynomial Sequences Conference · May 2018 · Stockholm
    On the asymptotic zero distribution of orthogonal polynomials on the unit circle with variable Verblunsky coefficients [slides]
  • Seminar talk at Ostrava University · February 2018 · Ostrava
    On the asymptotic eigenvalue distribution of Toeplitz matrices and generalizations [slides]
  • The Fifth Najman Conference on Spectral Theory and Differential Equations · September 2017 · Opatija
    On non-self-adjoint Toeplitz matrices with purely real spectrum [slides]
  • Methods of Algebra and Functional Analysis in Applications, summer school · July 2017 · Děčín
    An invitation to the non-self-adjoint church [slides]
  • Symmetries of Discrete Systems and Processes · June 2017 · Děčín
    Non-self-adjoint Toeplitz matrices with real spectrum and related orthogonal polynomials [slides]
  • International Conference on Special Functions: Theory, Computation, and Applications · June 2017 · Hong Kong
    Non-self-adjoint Toeplitz matrices with purely real spectrum and related problems [slides]
  • Analysis Group Seminar · November 2016 · Stockholm
    The moment problem [slides]
  • Operator Theory, Analysis and Mathematical Physics · August 2016 · Saint Petersburg
    Spectral analysis of some doubly infinite Jacobi matrices via characteristic function [slides]
  • The 26th International Conference in Operator Theory · June 2016 · Timisoara
    Spectral analysis of certain doubly infinite Jacobi matrices via characteristic function [slides]
  • Workshop on Operator Theory, Complex Analysis, and Applications · June 2016 · Coimbra
    Spectral analysis of non-self-adjoint Jacobi operator associated with Jacobian elliptic functions [slides]
  • Quantum Circle Seminar · March 2016 · Prague
    On the localization of spectra of complex sampling Jacobi matrices and open problems [slides]
  • Spectral Theory and Applications · March 2016 · Stockholm
    Spectral analysis of two doubly infinite Jacobi operators [slides]
  • Young Researchers Workshop on Spectral Theory · October 2015 · Bern
    Spectral analysis of a complex Jacobi matrix associated with Jacobian elliptic functions [slides]
  • Methods of Algebra and Functional Analysis in Applications, summer school · August 2015 · Telč
    On the Ising spin model [slides]
  • Symmetries of Discrete Systems and Processes · August 2015 · Děčín
    Nevanlinna extremal measures for polynomials related to q-Fibonacci polynomials [slides]
  • School on Theoretical Informatics, Graphs and Mathematics · May 2015 · Kruh u Jilemnice
    How Pusheen uses computers to do mathematics [slides]
  • Conference on Mathematics and Applications · November 2014 · Kuwait City
    On certain function with applications concerning tridiagonal matrices [slides]
  • Operator Theory, Analysis and Mathematical Physics · July 2014 · Stockholm
    The Nevanlinna parametrization and orthogonality relations for q-Lommel polynomials in the indeterminate case [slides]
  • Combinatorics on Words and Mathematical Physics, · May 2014 · Kruh u Jilemnice
    Introduction to the Theory of Orthogonal Polynomials [slides]
    Nevanlinna functions and orthogonality relations for q-Lommel polynomials [slides]
  • International Workshop on Operator Theory and Its Applications · December 2013 · Bangalore
    The characteristic function for infinite Jacobi matrices, the spectral zeta function, and solvable examples [slides]
  • Formal and Analytic Solutions of Differential, Difference and Discrete Equations · August 2013 · Bedlewo
    Constructing measures of orthogonality with applications [slides]
  • Combinatorics on Words and Mathematical Physics, · May 2013 · Dolní Lomná
    One-parameter Generalization of Some Classes of Orthogonal Polynomials [slides]
    Continued Fractions Appearing Naturally in Spectral Analysis of Jacobi Operators [slides]
  • Seminar at Nuclear Physics Institute ASCR · May 2013 · Řež u Prahy
    Moment Problem [slides]
  • Seminar at Institute of Theoretical Physics, University of Wroclaw · November 2012 · Wroclaw
    Spectral Analysis of Jacobi Operators and Related Problems [slides]
  • Operator Theory, Analysis and Mathematical Physics Conference · June 2012 · Barcelona
    Recent Progress on Spectral Analysis of Jacobi Matrices and Related Problems [slides]
  • Combinatorics on Words and Mathematical Physics · May 2012 · Svatý Ján pod Skalou
    The Characteristic Function for Jacobi Matrices with Applications [slides]
  • 22nd International Workshop on Operator Theory and its Applications · July 2011 · Sevilla
    On the Eigenvalue Problem for a Certain Class of Jacobi Matrices [slides]
  • Combinatorics on Words and Mathematical Physics · May 2011 · Fryšava
    On Function F and the Eigenvalue Problem for a Certain Class of Jacobi Matrices [slides]
  • Fourth School and Workshop on "Mathematical Methods in Quantum Mechanics" · February 2011 · Bressanone
    On the Eigenvalue Problem for a Certain Class of Infinite Jacobi Matrices [slides]
  • QMath11 Mathematical Results in Quantum Physics · September 2010 · Hradec Králové
    On the Eigenvalue Problem for a Particular Class of Jacobi Matrices [slides]

Organized meetings