相关论文: On the commutation properties of finite convolutio…

The commutation relation $KL = LK$ between finite convolution integral operator $K$ and differential operator $L$ has implications for spectral properties of $K$. We characterize all operators $K$ admitting this commutation relation. Our…

Spectral properties of many finite convolution integral operators have been understood by finding differential operators that commute with them. In this paper we compile a complete list of such commuting pairs, extending previous work to…

In this paper, we construct some examples of commuting differential operators $L_1$ and $L_2$ with rational coefficients of rank 3 corresponding to a curve of genus 2.

Representations by linear integral operators on $L_p$ spaces over measure spaces are investigated for the polynomial covariance type commutation relations and more general two-sided generalizations of covariance commutation relations…

We review the basic properties of paired operators and their adjoints, the transposed paired operators, with particular reference to commutation relations, and we study the properties of their kernels, bringing out their similarities and…

In the article we study properties of the random integral operator in $L_2(\mathbb{R})$ whose kernel is obtained as a convolution of Gaussian density with a stationary point process.

Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…

We study a system of partial differential equations defined by commuting family of differential operators with regular singularities. We construct ideally analytic solutions depending on a holomorphic parameter. We give some explicit…

We give definitions and some properties of the shift operator S_{L(H^2)} and multiplication operator on L(H^2). In addition, we obtain some properties of the commutant of the shift operator S_{L(H^2)} and characterize S_{L(H^2)}-invariant…

In this paper we study commuting difference operators of rank two. We introduce an equation on potentials $V(n),W(n)$ of the difference operator $L_4=(T+V(n)T^{-1})^2+W(n)$ and some additional data. With the help of this equation we find…

Different finite difference replacements for the derivative are analyzed in the context of the Heisenberg commutation relation. The type of the finite difference operator is shown to be tied to whether one can naturally consider $P$ and $X$…

Commuting is an important property in many cases of investigation of properties of operators as well as in various applications, especially in quantum physics. Using the observation that the generalized weighted differential operator of…

Representations of polynomial covariance type commutation relations by linear integral operators on $L_p$ over measures spaces are investigated. Necessary and sufficient conditions for integral operators to satisfy polynomial covariance…

In this paper we offer a computational approach to the spectral function for a finite family of commuting operators, and give applications. Motivated by questions in wavelets and in signal processing, we study a problem about spectral…

A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…

An L-basis associated to a linear second-order ordinary differential operator L is an infinite sequence of functions {\phi_k}_{k=0}^{\infty} such that L\phi_k=0 for k=0,1, L\phi_k=k(k-1)\phi_{k-2}, for k=2,3,... and all \phi_k satisfy…

In this paper we study the commutators of fractional type integral operators. This operators are given by kernels of theform $$K(x,y)=k_1(x-A_1y)k_2(x-A_2y)\dots k_m(x-A_my),$$ where $A_i$ are invertibles matrices and each $k_i$ satisfies a…

We find an explicit integral formula for the eigenfunctions of a fourth order differential operator against the kernel involving two Bessel functions. Our formula establishes the relation between K-types in two different realizations of the…

Suppose that $\Gamma$ is a continuous and self-adjoint Hankel operator on $L^2(0, \infty)$ and that $Lf=-(d/dx(a(x)df/dx))+b(x)f(x)$ with $a(0)=0$. If $a$ and $b$ are both quadratic, hyperbolic or trigonometric functions, and $\phi$…

For Belavin's elliptic quantum R-matrix, we construct an L-operator as a set of difference operators acting on functions on the type A weight space. According to the fundamental relation $RLL=LLR$, the trace of the L-operator gives a…