About me

Publications

Talks

Posters

Journals

Links

 

Last update:
        09-07-2017

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 a Postdoc at Department of Mathematics at Stockholm University, Assistant Professor "on leave" at Department of Applied Mathematics of the Faculty of Information Technology at Czech Technical University in Prague, and member of MAFIA group.

 Office:     Stockholm University
Department of Mathematics
Kräftriket, house no. 5
Room number 210
SE - 106 91 Stockholm
Sweden
 Email:     stampach@math.su.se
stampfra@fit.cvut.cz

                                                                               

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

My Curiculum Vitae and my Doctoral Thesis.

Publications

  1. B. Shapiro, F. Štampach, Non-self-adjoint Toeplitz matrices whose principal submatrices have real spectrum, submitted [arXiv].
  2. M. E. H. Ismail, F. Štampach, Spectral analysis of two doubly infinite Jacobi matrices with exponential entries, submitted [arXiv].
  3. P. Siegl, F. Štampach, Spectral analysis of non-self-adjoint Jacobi operator associated with Jacobian elliptic functions, in press in Oper. Matrices, (2017) [arXiv].
  4. F. Štampach, The characteristic function for complex doubly infinite Jacobi matrices, to appear in Integr. Equ. Oper. Theory, (2017) [arXiv, doi].
  5. F. Štampach, P. Šťovíček, Factorization of the characteristic function of a Jacobi matrix, Oper. Matrices 11 (2017) 147-169 [arXiv, doi].
  6. P. Siegl, F. Štampach, On extremal properties of Jacobian elliptic functions with complex modulus, Math. Anal. Appl. 442 (2016) 627-641 [arXiv, doi].
  7. F. Štampach, Nevanlinna extremal measures for polynomials related to q-1-Fibonacci polynomials, Adv. Appl. Math. 78 (2016) 56-75 [arXiv, doi].
  8. F. Štampach, P. Šťovíček, The Nevanlinna parametrization for q-Lommel polynomials in the indeterminate case, J. Approx. Theor. 201 (2016) 48-72 [arXiv, doi].
  9. F. Štampach, P. Šťovíček, Special functions and spectrum of Jacobi matrices, Linear Alg. Appl. 464 (2015) 38-61 [arXiv, doi].
  10. 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].
  11. F. Štampach, P. Šťovíček, Orthogonal polynomials associated with Coulomb wave functions, Math. Anal. Appl. 419 (2014) 231-254 [arXiv, doi].
  12. F. Štampach, P. Šťovíček, The characteristic function for Jacobi matrices with applications, Linear Alg. Appl. 438 (2013) 4130-4155 [arXiv, doi].
  13. 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].


Talks

Here is a list of several talks I gave.

  • 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]

Posters

Here is a list of several posters presented at conferences.

  • July 2013, Sapporo, The 6th Pacific RIM Conference on Mathematics,
          poster: One-parameter Generalization of Charlier and Al-Salam-Carlitz Polynomials [poster]
  • August 2012, Aalborg, International Congres of Mathematical Physics,
          poster: The Characteristic Function for Complex Jacobi Matrices [poster]
  • June 2011, Dresden, Quantum Physics with Non-Hermitian Operators,
          poster: Some Results on the Spectrum of Complex Jacobi Operators [poster]
  • November 2010, Marseille, Quantum Dynamics International Conference in Honor of Pierre Duclos,
          poster: On a Characteristic Function of a Certain Class of Jacobi Matrices [poster]

Journals reffereed for:

Links

  • MAFIA group - research group at department of mathematics at FNSPE
  • Askey-scheme - comprehensive list of classical orthogonal polynomials and their q-analogues
  • Abramowitz and Stegun - Handbook of Mathematical Functions
  • DLMF - Digital Library of Mathematical Functions
  • Wolfram functions site - useful while working with special functions
  • Gerald Teschl - very nice free lectrure notes available at the webpage
  • Doppler Institute - institute for mathematical physics and applied mathematics
  • Pavel Exner - home page of Professor Exner
  • FAQM - Frequently Asked Questions in Mathematics