Related papers: Generalized discrete integrable operator and integ…
We study integro-differential inclusions in Hilbert spaces with operator-valued kernels and give sufficient conditions for the well-posedness. We show that several types of integro-differential equations and inclusions are covered by the…
We introduce the notions of kernel map and kernel set of a bounded linear operator on a Hilbert space relative to a subspace lattice. The characterization of the kernel maps and kernel sets of finite rank operators leads to showing that…
In this article, we define discrete analogue of generalized Hardy spaces and its separable subspace on a homogenous rooted tree and study some of its properties such as completeness, inclusion relations with other spaces, separability,…
We construct a 2-category of differential graded schemes. The local affine models in this theory are differential graded algebras, which are graded commutative with unit over a field of characteristic zero, are concentrated in non-positive…
In this paper we develop a new approach for studying differential operators of an isolated singularity graded hypersurface ring $R$ defining a surface in affine three-space over a field of characteristic zero. With this method, we construct…
Given a smooth proper morphism $f\colon X\rightarrow S$, we introduce a certain derived category where morphisms are permitted to be $\mathcal{O}_S$-linear differential operators. We then prove a generalisation of Serre duality that applies…
We study Fredholm determinants of a class of integral operators, whose kernels can be expressed as double contour integrals of a special type. Such Fredholm determinants appear in various random matrix and statistical physics models. We…
The present paper contains two interrelated developments. First, are proposed new generalized Verma modules. They are called k-Verma modules, k\in N, and coincide with the usual Verma modules for k=1. As a vector space a k-Verma module is…
We introduce a new class of fully nonlinear integro-differential operators with possible nonsymmetric kernels, which includes the ones that arise from stochastic control problems with purely jump L\`evy processes. If the index of the…
We decompose the discrete bilinear spherical averaging operator into simpler operators in several ways. This leads to a wide array of extensions, such as to the simplex averaging operator, and applications, such as to operator bounds.
A method of generating differential operators is used to solve the spectral problem for a generalisation of the Sylvester-Kac matrix. As a by-product, we find a linear differential operator with polynomial coefficients of the first order…
We introduce a classification of simple, regular, closed symmetric operators with deficiency indices (1,1) according to a geometric criterion that extends the classical notions of entire operators and entire operators in the generalized…
It is known that determinantal point processes have an intimate relation to operator algebras. In the paper, we extend this relationship to encompass dynamical aspects. Especially, we delve into two types of determinantal point processes.…
We develop a duality for operations on nested pairs of modules that generalizes the duality between absolute interior operations and residual closure operations from [ER21], extending our previous results to the expanded context. We apply…
Matrices over the dual numbers are considered. We propose an approach to classify these matrices up to similarity. Some preliminary results on the realization of this approach are obtained. In particular, we produce explicitly canonical…
The continuity of the core inverse and the dual core inverse is studied in the setting of C*-algebras. Later, this study is specialized to the case of bounded Hilbert space operators and to complex matrices. In addition, the…
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…
Multilevel methods are among the most efficient numerical methods for solving large-scale linear systems that arise from discretized partial differential equations. The fundamental module of such methods is a two-level procedure, which…
Dunkl operators are differential-difference operators parametrized by a finite reflection group and a weight function. The commutative algebra generated by these operators generalizes the algebra of standard differential operators and…
The equivalence problem for linear differential operators of the second order, acting in vector bundles, is discussed. The field of rational invariants of symbols is described and connections, naturally accosiated with differential…