One Condition for Discreteness of the Spectrum and Compactness of the Resolvent of a Nonsectorial Sturm–Liouville Operator on a Semiaxis

IF 0.5 4区数学 Q3 MATHEMATICS

Doklady Mathematics Pub Date : 2023-08-30 DOI:10.1134/S1064562423700734

S. N. Tumanov

引用次数: 0

Abstract

The spectral properties of the Sturm–Liouville operator on a semiaxis in the case of a complex-valued potential with a range exceeding the half-plane have been poorly studied. The operator in this case can be nonsectorial: its numerical range can coincide with the entire complex plane. In this situation, conditions are proposed ensuring the discreteness of the spectrum and the compactness of the resolvent.

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半轴上非扇形Sturm-Liouville算子谱离散性和解紧性的一个条件

对于范围超过半平面的复值势在半轴上的Sturm-Liouville算符的谱性质研究得很少。在这种情况下，运算符可以是非扇形的:它的数值范围可以与整个复平面重合。在这种情况下，提出了保证谱的离散性和解的紧密性的条件。

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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来源期刊

Doklady Mathematics 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3-6 weeks

期刊介绍： Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.