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pro vyhledávání: '"Šťovíček, Pavel"'
Autor:
Šťovíček, Pavel, Świderski, Grzegorz
We consider positive Jacobi matrices $J$ with compact inverses and consequently with purely discrete spectra. A number of properties of the corresponding sequence of orthogonal polynomials is studied including the convergence of their zeros, the vagu
Externí odkaz:
http://arxiv.org/abs/2409.19644
Autor:
Šťovíček, Pavel
Publikováno v:
J. Math. Phys. 65, 023503 (2024)
A series of the form $\sum_{\ell=0}^{\infty}c(\kappa,\ell)\,M_{\kappa,\ell+1/2}(r_{0})W_{\kappa,\ell+1/2}(r)P_{\ell}(\cos(\gamma))$ is evaluated explicitly where $c(\kappa,\ell)$ are suitable complex coefficients, $M_{\kappa,\mu}$ and $W_{\kappa,\mu}
Externí odkaz:
http://arxiv.org/abs/2403.03749
Autor:
Stovicek, Pavel
Assume that $\{a_{n};\,n\geq0\}$ is a sequence of positive numbers and $\sum a_{n}^{\,-1}<\infty$. Let $\alpha_{n}=ka_{n}$, $\beta_{n}=a_{n}+k^{2}a_{n-1}$ where $k\in(0,1)$ is a parameter, and let $\{P_{n}(x)\}$ be an orthonormal polynomial sequence
Externí odkaz:
http://arxiv.org/abs/2203.05350
Autor:
Štampach, František, Šťovíček, Pavel
A semi-infinite weighted Hankel matrix with entries defined in terms of basic hypergeometric series is explicitly diagonalized as an operator on $\ell^{2}(\mathbb{N}_{0})$. The approach uses the fact that the operator commutes with a diagonalizable J
Externí odkaz:
http://arxiv.org/abs/2112.06035
Autor:
Štampach, František, Šťovíček, Pavel
Four new examples of explicitly diagonalizable Hankel matrices depending on a parameter $k\in(0,1)$ are presented. The Hankel matrices are regarded as matrix operators on the Hilbert space $\ell^{2}(\mathbb{N}_{0})$ and the solution of the spectral p
Externí odkaz:
http://arxiv.org/abs/1911.08218
Autor:
Štampach, František, Šťovíček, Pavel
A complete characterization is provided of Hankel matrices commuting with Jacobi matrices which correspond to hypergeometric orthogonal polynomials from the Askey scheme. It follows, as the main result of the paper, that the generalized Hilbert matri
Externí odkaz:
http://arxiv.org/abs/1911.07059
Autor:
Stovicek, Pavel
Let $\{\hat{P}_{n}(x)\}$ be an orthonormal polynomial sequence and denote by $\{w_{n}(x)\}$ the respective sequence of functions of the second kind. Suppose the Hamburger moment problem for $\{\hat{P}_{n}(x)\}$ is determinate and denote by $J$ the co
Externí odkaz:
http://arxiv.org/abs/1904.13199
Autor:
Štampach, František, Šťovíček, Pavel
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 commutant of Jacobi matrices associated with orthogonal polynomials from
Externí odkaz:
http://arxiv.org/abs/1811.05820
Autor:
Stovicek, Pavel
A non-relativistic quantum model is considered with a point particle carrying a charge $e$ and moving on the plane pierced by two infinitesimally thin Aharonov-Bohm solenoids and subjected to a perpendicular uniform magnetic field of magnitude $B$. R
Externí odkaz:
http://arxiv.org/abs/1611.06942
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