Related papers: Dispersion Estimates for the Discrete Laguerre Ope…
Exceptional Laguerre-type differential expressions make up an infinite class of Schr\"odinger operators having rational potentials and one limit-circle endpoint. In this manuscript, the spectrum of all self-adjoint extensions for a general…
We identify a class of non-local integro-differential operators $K$ in $\mathbb{R}$ with Dirichlet-to-Neumann maps in the half-plane $\mathbb{R} \times (0, \infty)$ for appropriate elliptic operators $L$. More precisely, we prove a…
We study degenerate Whittaker vectors in scalar type holomorphic discrete series representations of tube type Hermitian Lie groups and their analytic continuation. In four different realizations, the bounded domain picture, the tube domain…
We are interested in the asymptotic behavior of orthogonal polynomials of the generalized Jacobi type as their degree $n$ goes to $\infty$. These are defined on the interval $[-1,1]$ with weight function…
In this paper we construct Donoghue $m$-functions for the Jacobi differential operator in $L^2\big((-1,1); (1-x)^{\alpha} (1+x)^{\beta} dx\big)$, associated to the differential expression \begin{align*} \begin{split} \tau_{\alpha,\beta} = -…
We find the intervals $[\alpha, \beta (\alpha)]$ such that if a univariate real polynomial or entire function $f(z) = a_0 + a_1 z + a_2 z^2 + \cdots $ with positive coefficients satisfy the conditions $ \frac{a_{k-1}^2}{a_{k-2}a_{k}} \in…
In this paper we consider the 1D Schr\"odinger operator $H$ with periodic point interactions. We show an $L^1-L^\infty$ bound for the time evolution operator $e^{-itH}$ restricted to each energy band with decay order $O(t^{-1/3})$ as $t\to…
We set out to build a framework for self-adjoint extension theory for powers of the Jacobi differential operator that does not make use of classical deficiency elements. Instead, we rely on simpler functions that capture the impact of these…
Using the representation theory of sl(2) and an appropriate model for tensor product of lowest weight Verma modules, we give a realisation first of the Hahn algebra, and then of the Racah algebra, using Jacobi differential operators. While…
The discrete orthogonality relations hold for all the orthogonal polynomials obeying three term recurrence relations. We show that they also hold for multi-indexed Laguerre and Jacobi polynomials, which are new orthogonal polynomials…
We investigate Lie-Trotter product formulae for abstract nonlinear evolution equations with delay. Using results from the theory of nonlinear contraction semigroups in Hilbert spaces, we explain the convergence of the splitting procedure.…
In this paper we commence the study of discrete harmonic analysis associated with Jacobi orthogonal polynomials of order $(\alpha,\beta)$. Particularly, we give the solution $W^{(\alpha,\beta)}_t$, $t\ge 0$, and some properties of the heat…
We consider the Jacobi operator (T,D(T)) associated with an indeterminate Hamburger moment problem, and present countable subsets S of the domain D(T) such that span(S) is dense in \ell^2. As an example we have…
We prove H\"older regularity results for a class of nonlinear elliptic integro-differential operators with integration kernels whose ellipticity bounds are strongly directionally dependent. These results extend those in [9] and are also…
Let $G$ be a semisimple, connected, and noncompact Lie group with a finite center. We carry out a detailed analysis of oscillating integrals involving the Harish-Chandra $c$-function, in the case of real rank $l\ge 2$. This allows to obtain…
The distribution function for the first eigenvalue spacing in the Laguerre unitary ensemble of finite size may be expressed in terms of a solution of the fifth Painleve transcendent. The generating function of a certain discontinuous linear…
Explicit coupling property and gradient estimates are investigated for the linear evolution equations on Hilbert spaces driven by an additive cylindrical L\'evy process. The results are efficiently applied to establish the exponential…
We study the $\ell^\infty \to \ell^\infty$ operator norm of products of independent random matrices with independent and identically distributed entries. For $n$-by-$n$ matrices whose entries are centered, have unit variance, and have a…
On $\mathbb{R}^d_+$, endowed with the Laguerre probability measure $\mu_\alpha$, we define a Hodge-Laguerre operator $\mathbb{L}_\alpha=\delta\delta^*+\delta^* \delta$ acting on differential forms. Here $\delta$ is the Laguerre exterior…
Asymptotic approximations of Jacobi polynomials are given for large values of the $\beta$-parameter and of their zeros. The expansions are given in terms of Laguerre polynomials and of their zeros. The levels of accuracy of the…