František Štampach

This webpage is devoted to my academic activities. Its main aim is to provide basic information about me and to share sources with scientific content.

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).

Preprints

  1. F. Štampach, J. Waclawek: Optimal discrete p-Hardy-Rellich-Birman inequalities, preprint [arXiv].
  2. F. Štampach, J. Waclawek: The p-Hardy-Rellich-Birman inequalities on the half-line, preprint [arXiv].
  3. A. Pushnitski, F. Štampach: Schrödinger operators on the half-line with integrable complex potentials, preprint [arXiv].
  4. R. Kozhan, F. Štampach: Ratio asymptotics and zero density for orthogonal polynomials with varying Verblunsky coefficients, preprint [arXiv].

Articles in journals

  1. A. Pushnitski, F. Štampach: The Borg-Marchenko uniqueness theorem for complex potentials, accepted in J. Math. Pures Appl. (2026) [arXiv].
  2. F. Štampach, J. Waclawek: Optimal discrete Hardy-Rellich-Birman inequalities, accepted in J. Anal. Math. (2026) [arXiv].
  3. F. Štampach, J. Waclawek: A Herglotz-Nevanlinna function from the optimal discrete p-Hardy weight, Proc. Amer. Math. Soc. 154 (2026) 807-819 [arXiv, doi].
  4. 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 [arXiv, doi].
  5. 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 [arXiv, doi].
  6. B. Gerhat, D. Krejčiřík, F. Štampach: An improved discrete Rellich inequality on the half-line, Israel J. Math. 268 (2025) 45-72 [arXiv, doi].
  7. M. Jex, F. Štampach: On the ground state of lattice Schrödinger operators, J. Spectr. Theory 15 (2025) 647-678 [arXiv, doi].
  8. A. Pushnitski, F. Štampach: A functional model and tridiagonalisation for symmetric anti-linear operators, J. Operator Theory 95 (2024) 101-128 [arXiv, doi].
  9. A. Pushnitski, F. Štampach: An inverse spectral problem for non-self-adjoint Jacobi matrices, Int. Math. Res. Not. 2024 (2024) 6106-6139 [arXiv, doi].
  10. P. Blaschke, F. Štampach: Asymptotic root distribution of Charlier polynomials with large negative parameter, J. Math. Anal. Appl. 524 (2023) 1-29 [arXiv, doi].
  11. F. Štampach: Asymptotic spectral properties of the Hilbert L-matrix, SIAM J. Matrix Anal. Appl. 43 (2022) 1658-1679 [arXiv, doi].
  12. 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].
  13. F. Štampach: The Hilbert L-matrix, J. Funct. Anal. 282 (2022) 1-46 [arXiv, doi].
  14. 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].
  15. 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].
  16. 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].
  17. F. Štampach: Asymptotic behaviour and zeros of the Bernoulli polynomials of the second kind, J. Approx. Theory 262, (2021) 1-28 [arXiv, doi].
  18. 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]] [arXiv, doi].
  19. 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].
  20. 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].
  21. F. Štampach, P. Šťovíček: On Hankel matrices commuting with Jacobi matrices from the Askey scheme, Linear Alg. Appl. 591 (2020) 235-267 [arXiv, doi].
  22. O. O. Ibrogimov, F. Štampach: Spectral enclosures for non-self-adjoint discrete Schrödinger operators, Integr. Equ. Oper. Theory 91 (2019) 1-15 [arXiv, doi].
  23. 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].
  24. 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].
  25. 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) [arXiv, doi, doi].
  26. 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].
  27. 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].
  28. F. Štampach: The characteristic function for complex doubly infinite Jacobi matrices, Integr. Equ. Oper. Theory 88 (2017) 501-534 [arXiv, doi].
  29. F. Štampach, P. Šťovíček: Factorization of the characteristic function of a Jacobi matrix, Oper. Matrices 11 (2017) 147-169 [arXiv, doi].
  30. P. Siegl, F. Štampach: On extremal properties of Jacobian elliptic functions with complex modulus, J. Math. Anal. Appl. 442 (2016) 627-641 [arXiv, doi].
  31. F. Štampach: Nevanlinna extremal measures for polynomials related to q^-1-Fibonacci polynomials, Adv. Appl. Math. 78 (2016) 56-75 [arXiv, doi].
  32. F. Štampach, P. Šťovíček: The Nevanlinna parametrization for q-Lommel polynomials in the indeterminate case, J. Approx. Theory 201 (2016) 48-72 [arXiv, doi].
  33. F. Štampach, P. Šťovíček: Special functions and spectrum of Jacobi matrices, Linear Alg. Appl. 464 (2015) 38-61 [arXiv, doi].
  34. 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].
  35. F. Štampach, P. Šťovíček: Orthogonal polynomials associated with Coulomb wave functions, J. Math. Anal. Appl. 419 (2014) 231-254 [arXiv, doi].
  36. F. Štampach, P. Šťovíček: The characteristic function for Jacobi matrices with applications, Linear Alg. Appl. 438 (2013) 4130-4155 [arXiv, doi].
  37. 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

  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 [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]

Talks

Here is a list of several talks I gave.

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

Organized meetings