Zobrazeno 1 - 10
of 64
pro vyhledávání: '"Stampach, Frantisek"'
Autor:
Štampach, František, Waclawek, Jakub
We prove sufficient conditions on a parameter sequence to determine optimal weights in inequalities for an integer power $\ell$ of the discrete Laplacian on the half-line. By a concrete choice of the parameter sequence, we obtain explicit optimal dis
Externí odkaz:
http://arxiv.org/abs/2405.07742
We consider the class of bounded symmetric anti-linear operators $B$ with a cyclic vector. We associate with $B$ the spectral data consisting of a probability measure and a function. In terms of the spectral data of $B$, we introduce a functional mod
Externí odkaz:
http://arxiv.org/abs/2402.01237
Autor:
Jex, Michal, Štampach, František
We prove necessary and sufficient conditions for lattice Schr\"{o}dinger operators to have a zero energy bound state in arbitrary dimension. The two criteria are sharp, complementary, and depend crucially on both the dimension and asymptotic behaviou
Externí odkaz:
http://arxiv.org/abs/2312.08081
We study the criticality and subcriticality of powers $(-\Delta)^\alpha$ with $\alpha>0$ of the discrete Laplacian $-\Delta$ acting on $\ell^2(\mathbb{N})$. We prove that these positive powers of the Laplacian are critical if and only if $\alpha \ge
Externí odkaz:
http://arxiv.org/abs/2307.09919
We consider the class of bounded symmetric Jacobi matrices $J$ with positive off-diagonal elements and complex diagonal elements. With each matrix $J$ from this class, we associate the spectral data, which consists of a pair $(\nu,\psi)$. Here $\nu$
Externí odkaz:
http://arxiv.org/abs/2305.19608
Autor:
Blaschke, Petr, Štampach, František
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. We determine implicit equations for these curves and deduce the limitin
Externí odkaz:
http://arxiv.org/abs/2210.16922
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-like inequalities and formulate an open problem for the discrete Rell
Externí odkaz:
http://arxiv.org/abs/2206.11007
Autor:
Štampach, František
We study asymptotic spectral properties of the generalized Hilbert $L$-matrix \[ L_{n}(\nu)=\left(\frac{1}{\max(i,j)+\nu}\right)_{i,j=0}^{n-1}, \] for large order $n$. First, for general $\nu\neq0,-1,-2,\dots$, we deduce the asymptotic distribution o
Externí odkaz:
http://arxiv.org/abs/2202.04116
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
Publikováno v:
Bull. London. Math. Soc. 54 (2022) 2379-2403
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 spectral enclosures are obtained for summable potentials. Second, general
Externí odkaz:
http://arxiv.org/abs/2111.08265