20 citations · 73 across the 18 of their papers we have counts for
22 papers
Optimal Hardy weights for the fractional discrete Dirichlet Laplacian on the half-line
František Štampach, Jakub Waclawek
For positive powers of the discrete Dirichlet Laplacian , non-trivial Hardy weights exist if and only if . For , an explicit optimal Hardy…
Optimal fractional discrete Hardy inequalities on the half-line
František Štampach, Jakub Waclawek
We consider a Toeplitz realisation of the fractional discrete Laplacian on the half-line as a compression of the full-line fractional discrete Laplacian to $\…
On Lieb-Thirring inequalities for multidimensional Schrödinger operators with complex potentials
Sabine Bögli, Sukrid Petpradittha, František Štampach
We solve the open problem by Demuth, Hansmann, and Katriel announced in [Integr. Equ. Oper. Theory 75 (2013), 1-5] by a counter-example construction. The problem concerns a possibl…
On the ground state of lattice Schrödinger operators
Michal Jex, František Štampach
We prove necessary and sufficient conditions for lattice Schrödinger operators to have a zero energy bound state in arbitrary dimension. The two criteria are sharp, complementary,…
Criticality transition for positive powers of the discrete Laplacian on the half line
Borbala Gerhat, David Krejcirik, Frantisek Stampach
We study the criticality and subcriticality of powers with of the discrete Laplacian acting on . We prove that these positive powers of the…
Asymptotic root distribution of Charlier polynomials with large negative parameter
Petr Blaschke, František Štampach
We analyze the asymptotic distribution of roots of Charlier polynomials with negative parameter depending linearly on the index. The roots cluster on curves in the complex plane. W…
An improved discrete Rellich inequality on the half-line
Borbala Gerhat, David Krejcirik, Frantisek Stampach
Based on a new idea of factorization, we prove an improved discrete Rellich inequality and discuss its optimality. We also give a conjecture on improved higher order discrete Hardy…
Spectral enclosures and stability for non-self-adjoint discrete Schroedinger operators on the half-line
David Krejcirik, Ari Laptev, Frantisek Stampach
We make a spectral analysis of discrete Schroedinger operators on the half-line, subject to complex Robin-type boundary couplings and complex-valued potentials. First, optimal spec…
A sharp form of the discrete Hardy inequality and the Keller-Pinchover-Pogorzelski inequality
David Krejcirik, Frantisek Stampach
We give a short proof of a recently established Hardy-type inequality due to Keller, Pinchover, and Pogorzelski together with its optimality. Moreover, we identify the remainder te…
New family of symmetric orthogonal polynomials and a solvable model of a kinetic spin chain
Tomáš Kalvoda, František Štampach
We study an infinite one-dimensional Ising spin chain where each particle interacts only with its nearest neighbors and is in contact with a heat bath with temperature decaying hyp…
New explicitly diagonalizable Hankel matrices related to the Stieltjes-Carlitz polynomials
František Štampach, Pavel Šťovíček
Four new examples of explicitly diagonalizable Hankel matrices depending on a parameter are presented. The Hankel matrices are regarded as matrix operators on the Hilbe…
On Hankel matrices commuting with Jacobi matrices from the Askey scheme
František Štampach, Pavel Šťovíček
A complete characterization is provided of Hankel matrices commuting with Jacobi matrices which correspond to hypergeometric orthogonal polynomials from the Askey scheme. It follow…
Location of eigenvalues of non-self-adjoint discrete Dirac operators
Biagio Cassano, Orif O. Ibrogimov, David Krejcirik +1
We provide quantitative estimates on the location of eigenvalues of one-dimensional discrete Dirac operators with complex -potentials for . As a corollar…
Spectral enclosures for non-self-adjoint discrete Schrödinger operators
Orif O. Ibrogimov, František Štampach
We study location of eigenvalues of one-dimensional discrete Schrödinger operators with complex -potentials for . In the case of -potentials…
Spectral representation of some weighted Hankel matrices and orthogonal polynomials from the Askey scheme
František Štampach, Pavel Šťovíček
We provide an explicit spectral representation for several weighted Hankel matrices by means of the so called commutator method. These weighted Hankel matrices are found in the com…
Factorization of the characteristic function of a Jacobi matrix
F. Stampach, P. Stovicek
In a recent paper a class of infinite Jacobi matrices with discrete character of spectra has been introduced. With each Jacobi matrix from this class an analytic function is associ…
The Nevanlinna parametrization for -Lommel polynomials in the indeterminate case
F. Štampach, P. Šťovíček
The Hamburger moment problem for the -Lommel polynomials which are related to the Hahn-Exton -Bessel function is known to be indeterminate for a certain range of parameters.…
The Hahn-Exton -Bessel function as the characteristic function of a Jacobi matrix
Frantisek Stampach, Pavel Stovicek
A family , , of semiinfinite positive Jacobi matrices is introduced with matrix entries taken from the Hahn-Exton -difference equation. The co…
Orthogonal polynomials associated with Coulomb wave functions
Frantisek Stampach, Pavel Stovicek
A class of orthogonal polynomials associated with Coulomb wave functions is introduced. These polynomials play a role analogous to that the Lommel polynomials do in the theory of B…
Special functions and spectrum of Jacobi matrices
Frantisek Stampach, Pavel Stovicek
Several examples of Jacobi matrices with an explicitly solvable spectral problem are worked out in detail. In all discussed cases the spectrum is discrete and coincides with the se…
The characteristic function for Jacobi matrices with applications
F. Stampach, P. Stovicek
We introduce a class of Jacobi operators with discrete spectra which is characterized by a simple convergence condition. With any operator J from this class we associate a characte…
On the eigenvalue problem for a particular class of finite Jacobi matrices
F. Stampach, P. Stovicek
A function with simple and nice algebraic properties is defined on a subset of the space of complex sequences. Some special functions are expressible in terms of $\m…