带有傅里叶-诺伊曼展开的算子的谱分析

IF 0.7 4区数学 Q2 MATHEMATICS

Complex Analysis and Operator Theory Pub Date : 2024-07-17 DOI:10.1007/s11785-024-01577-3

Krzysztof Stempak

引用次数: 0

摘要

我们对\(L^2(\mathbb {R}_+,dx)\) 上的斯特姆-利乌维尔算子进行了谱分析，通过利乌维尔变换，该算子等价于\(L^2(\mathbb {R},dx)\) 上具有重负势\(V(x)=-e^{2x}\) 的薛定谔算子。这一分析澄清了瓦罗纳在 1994 年提出的傅里叶-诺伊曼展开设置中的一些算子理论问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Spectral Analysis of an Operator with Fourier-Neumann Expansions Beneath

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Spectral Analysis of an Operator with Fourier-Neumann Expansions Beneath

We perform spectral analysis of a Sturm-Liouville operator on \(L^2(\mathbb {R}_+,dx)\) which, through the Liouville transformation, is unitarily equivalent to the Schrödinger operator on \(L^2(\mathbb {R},dx)\) with heavy negative potential \(V(x)=-e^{2x}\). This analysis clarifies some operator theory aspects of the setting of Fourier-Neumann expansions initiated by Varona in 1994.

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来源期刊

Complex Analysis and Operator Theory 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

107

审稿时长

3 months

期刊介绍： Complex Analysis and Operator Theory (CAOT) is devoted to the publication of current research developments in the closely related fields of complex analysis and operator theory as well as in applications to system theory, harmonic analysis, probability, statistics, learning theory, mathematical physics and other related fields. Articles using the theory of reproducing kernel spaces are in particular welcomed.