相关论文: Two-dimensional algebro-geometric difference opera…
This paper first introduces a new generalized inverse in Minkowski space, called the m-DMP inverse, and discusses its algebraic and geometrical properties. The second objective is to characterize the m-DMP inverse equivalently by ranges,…
In this paper, we give direct theorems on point wise and global approximation by new variants of Bernstein-Durrmeyer operator, introduced by A.-M. et al.[1].
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
Classification theorems for linear differential equations in two real variables, possessing eigenfunctions in the form of the polynomials (the generalized Bochner problem) are given. The main result is based on the consideration of the…
In this paper, we study the generalized differentiability of the metric projection operator in Hilbert spaces. We find exact expressions for Mordukhovich derivatives for the metric projection operator onto closed balls in Hilbert spaces and…
We introduce a notion of ``hereditarily antisymmetric'' operator algebras and prove a structure theorem for them in finite dimensions. We also characterize those operator algebras in finite dimensions which can be made upper triangular and…
We distinguish two classifications of bidifferential operators: between (A) spaces of modular forms and (B) spaces of weighted densities. (A) The invariant under the projective action of $\text{SL}(2;\mathbb{Z})$ binary differential…
A generalization of differential operators are pseudodifferential operators which are used for reasoning about partial differential equations with variable coefficients. A lot of useful properties about classical pseudodifferential…
Some algebraic, geometric and geometroalgebraic characteristics of pairs of operators are discussed.
We study mapping properties of two-dimensional linear integral operators in some weighted spaces with special kernels. The considered spaces are certain variant of Sobolev--Slobodetskii spaces and their generalizations related to Banach…
In this paper we consider a differential--difference system which is equivalent to the commutativity condition of two differential--difference operators. We study the rank two algebro--geometric solutions of this system.
One discovers why the solution of generalized umbral calculus difference nonhomogeneous equation in the form recently proposed by the author extends here now to generalized appellian delta operator and corresponding polynomials case almost…
This book aims to provide a brief overview of recent advancements in the theory of inverse problems for stochastic partial differential equations. In order to keep the content concise, we will only discuss the inverse problems of two…
We develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank $N$. It combines and unifies the ideas of Duistermaat-Gr\"unbaum and Wilson. Our construction is completely…
This article gives a fundamental discussion on variable coefficients, self-adjoint, formally partially hypoelliptic differential operators. A generalization of the results to pseudo differential operators, is given in a following article in…
In this work we obtain a version of the Procesi-Rasmyslov Theorem for the algebra of semi-invariants of representations of an arbitrary quiver with dimension vector (2,2,...,2).
We construct new infinite hierarchies of nonlocal symmetries and cosymmetries for the Krichever--Novikov equation using the inverse of the fourth-order recursion operator of the latter.
Several definitions of differential operators on modules over noncommutative rings are discussed.
This paper is devoted to a systematic study of certain geometric integral inequalities which arise in continuum combinatorial approaches to $L^p$-improving inequalities for Radon-like transforms over polynomial submanifolds of intermediate…
A differential geometrical and topological structure of Delsarte transmutation operators in multidimension is studied, the relationships with De Rham-Hodge-Skrypnik theory of generalized differential complexes is stated.