About me

Preprints

Publications

Grants

Talks

Journals

Links

 

Last update:
        14-06-2021

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.

 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@fjfi.cvut.cz
 ORCID iD:      0000-0003-3207-6010
 Scopus Author ID:      36648079100
 MR Author ID:      923972

                                                           
profile

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 Curiculum Vitae (not updated) and my Doctoral Thesis.


Publications

  1. S. Bögli, F. Štampach, On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators, to appear in J. Spectr. Theory (2021) [arXiv].
  2. 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].
  3. F. Štampach, Asymptotic behaviour and zeros of the Bernoulli polynomials of the second kind, J. Approx. Theory 262, (2021) 1-28 [arXiv, doi].
  4. 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]].
  5. 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].
  6. 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].
  7. F. Štampach, P. Šťovíček, On Hankel matrices commuting with Jacobi matrices from the Askey scheme, Linear Alg. Appl. 591 (2020) 235-267 [arXiv, doi].
  8. O. O. Ibrogimov, F. Štampach, Spectral enclosures for non-self-adjoint discrete Schrödinger operators, Integr. Equ. Oper. Theory 91 (2019) 1-15 [arXiv, doi].
  9. M. E. H. Ismail, F. Štampach, Spectral analysis of two doubly infinite Jacobi matrices with exponential entries, J. Func. Anal. 276 (2019) 1681-1716 [arXiv, doi].
  10. 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].
  11. B. Shapiro, F. Štampach, Non-self-adjoint Toeplitz matrices whose principal submatrices have real spectrum, Constr. Approx. 49 (2019) 191-226 [arXiv, doi].
  12. 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].
  13. 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].
  14. F. Štampach, The characteristic function for complex doubly infinite Jacobi matrices, Integr. Equ. Oper. Theory 88 (2017) 501-534 [arXiv, doi].
  15. F. Štampach, P. Šťovíček, Factorization of the characteristic function of a Jacobi matrix, Oper. Matrices 11 (2017) 147-169 [arXiv, doi].
  16. P. Siegl, F. Štampach, On extremal properties of Jacobian elliptic functions with complex modulus, J. Math. Anal. Appl. 442 (2016) 627-641 [arXiv, doi].
  17. F. Štampach, Nevanlinna extremal measures for polynomials related to q-1-Fibonacci polynomials, Adv. Appl. Math. 78 (2016) 56-75 [arXiv, doi].
  18. F. Štampach, P. Šťovíček, The Nevanlinna parametrization for q-Lommel polynomials in the indeterminate case, J. Approx. Theory 201 (2016) 48-72 [arXiv, doi].
  19. F. Štampach, P. Šťovíček, Special functions and spectrum of Jacobi matrices, Linear Alg. Appl. 464 (2015) 38-61 [arXiv, doi].
  20. 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].
  21. F. Štampach, P. Šťovíček, Orthogonal polynomials associated with Coulomb wave functions, J. Math. Anal. Appl. 419 (2014) 231-254 [arXiv, doi].
  22. F. Štampach, P. Šťovíček, The characteristic function for Jacobi matrices with applications, Linear Alg. Appl. 438 (2013) 4130-4155 [arXiv, doi].
  23. 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].


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.

  • 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]

Journals refereed for

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