Related papers: Bessel kernel determinants and integrable equation…
In this article we are interested in the differentiability property of the Markovian semi-group corresponding to the Bessel processes of nonnegative dimension. More precisely, for all $\delta \geq 0$ and $T>0$, we compute the derivative of…
When the number of particles is finite, the noncolliding Brownian motion (the Dyson model) and the noncolliding squared Bessel process are determinantal diffusion processes for any deterministic initial configuration $\xi=\sum_{j \in…
We consider matrix orthogonal polynomials related to Bessel type matrices of weights that can be defined in terms of a given matrix Pearson equation. From a Riemann-Hilbert problem we derive first and second order differential relations for…
This paper deals with the Sturm-Liouville problem that feature distribution potential, polynomial dependence on the spectral parameter in the first boundary condition, and analytical dependence, in the second one. We study an inverse…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator is…
We consider the gap probability for the Generalized Bessel process in the single-time and multi-time case. We prove that the scalar and matrix Fredholm determinants of such process can be expressed in terms of determinants of…
The aim of the present manuscript is to develop an index theory for singular Lagrangian systems, with a particular focus on the important class of singular operators given by Bessel type differential operators. The main motivation is to…
This is an inaugural study of the Dirichlet problem associated with a regular non-definite Sturm-Liouville equation in the case of two turning points. We give a priori lower bounds on the Richardson numbers associated with this problem…
In this study, we define discrete fractional Sturm-Liouville (DFSL) operators within Riemann-Liouville and Gr\"unwald-Letnikov fractional operators with both delta and nabla operators. We show selfadjointness of the DFSL operator for the…
In this paper we focus on qualitative properties of solutions to a nonlocal nonlinear partial integro-differential equation (PIDE). Using the theory of abstract semilinear parabolic equations we prove existence and uniqueness of a solution…
In this paper, Sturm-Liouville problem for difference equations is considered with potential function q(n). The representations of solutions are obtained by variation of parameters method. These solutions are proved, using summation by…
It is well established that the spectral analysis of canonically quantized four-dimensional Seiberg-Witten curves can be systematically studied via the Nekrasov-Shatashvili functions. In this paper, we explore another aspect of the relation…
This paper aims to study the q-analogue of the Sturm Liouville problem and to give an asymptotic behaviour at infinity for its solution '. Additionally, we establish an asymptotic expansion of the q-Bessel function $j_\alpha$ for $\alpha…
String equations related to 2D gravity seem to provide, quite naturally and systematically, integrable kernels, in the sense of Its-Izergin-Korepin and Slavnov. Some of these kernels (besides the "classical" examples of Airy and Pearcey)…
For a broad class of point processes, including determinantal point processes, we construct associated marked and conditional ensembles, which allow to study a random configuration in the point process, based on information about a randomly…
In this study, the theorem on necessary and sufficient conditions for the solvability of inverse problem for Sturm-Liouville operator with discontinuous coefficient is proved and the algorithm of reconstruction of potential from spectral…
The Bessel process models the local eigenvalue statistics near $0$ of certain large positive definite matrices. In this work, we consider the probability \begin{align*} \mathbb{P}\Big( \mbox{there are no points in the Bessel process on }…
The perturbation of the Sturm-Liouville operator on a finite interval with Dirichlet boundary conditions by a convolution operator is considered. Local stability and global unique solvability of the inverse problem of recovering the…
The inverse problem of recovery of a potential on a quantum tree graph from Weyl's matrix given at a number of points is considered. A method for its numerical solution is proposed. The overall approach is based on the leaf peeling method…
Partial inverse problems are studied for Sturm-Liouville operators with a discontinuity. The main results of the paper are local solvability and stability of the considered inverse problems. Our approach is based on a constructive algorithm…