Abstract

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.

中文翻译：

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带平移微分算子边值问题的轨迹符号与Fredholm性质

摘要

考虑边值问题，其中主算子和边界条件算子包括对应于离散群的作用的微分算子和移位算子。不假设考虑边值问题的流形是群不变的。给出了此类边值问题的轨迹符号的定义。结果表明，椭圆问题在相应的 Sobolev 空间中定义了 Fredholm 算子。给出了扩展和收缩问题的应用。