带移位微分算子边值问题的轨迹符号与Fredholm性质

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL Russian Journal of Mathematical Physics Pub Date : 2023-06-18 DOI:10.1134/S1061920823020012

A. V. Boltachev, A. Yu. Savin

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引用次数: 0

摘要

研究了一类边值问题，其中主算子和边界条件的算子包括与离散群的作用相对应的微分算子和移位算子。考虑边值问题的流形不被假定为群不变的。给出了这类边值问题的轨迹符号的定义。证明了椭圆型问题在相应的Sobolev空间中定义了Fredholm算子。给出了一个应用于扩展和收缩问题的方法。

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Trajectory Symbols and the Fredholm Property of Boundary Value Problems for Differential Operators with Shifts

Boundary value problems are considered in which the main operator and the operators of boundary conditions include differential and shift operators corresponding to the action of a discrete group. The manifold on which the boundary value problem is considered is not assumed to be group invariant. A definition of trajectory symbols for this class of boundary value problems is given. It is shown that elliptic problems define Fredholm operators in the corresponding Sobolev spaces. An application to problems with extensions and contractions is given.

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.