半轴上薛定谔算子的完全非自相接性

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2024-04-12 DOI:10.1090/spmj/1802

C. Fischbacher, S. Naboko, I. Wood

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引用次数: 0

摘要

本论文主要研究具有耗散约束势和耗散边界条件的半线上薛定谔算子的所有最大耗散扩展的完全非自相接性。研究表明，所有保留微分表达式的最大耗散扩展都是完全非自相接的。然而，最大耗散扩展有可能具有一维还原子空间，在该空间上的算子是自交的。本文给出了这些扩展和相应子空间的特征，并附有一个具体的例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Complete nonselfadjointness for Schrödinger operators on the semi-axis

This note is devoted to the study of complete nonselfadjointness for all maximally dissipative extensions of a Schrödinger operator on a half-line with dissipative bounded potential and dissipative boundary condition. It is shown that all maximally dissipative extensions that preserve the differential expression are completely nonselfadjoint. However, it is possible for maximally dissipative extensions to have a one-dimensional reducing subspace on which the operator is selfadjoint. A characterization of these extensions and the corresponding subspaces is given, accompanied by a specific example.

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.