薛定谔算子奇异连续谱中没有嵌入特征向量

IF 1.4 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2024-10-30 DOI:10.1007/s13324-024-00948-5

Kota Ujino

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引用次数: 0

摘要

一般来说，具有稀疏势的薛定谔算子具有奇异连续谱，而某个开放区间是纯奇异连续谱。我们给出一个充分条件，使开放区间的端点不是特征值。我们给出了一个半线上具有负稀疏势的薛定谔算子的例子，该算子在任何边界条件下都没有非负的嵌入特征值。

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No eigenvectors embedded in the singular continuous spectrum of Schrödinger operators

In general a Schrödinger operator with a sparse potential has singular continuous spectrum, and some open interval is purely singular continuous spectrum. We give a sufficient condition so that the endpoint of the open interval is not an eigenvalue. An example of a Schrödinger operator with a negative sparse potential on the half-line which has no nonnegative embedded eigenvalue for any boundary conditions is given.

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来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

期刊介绍： Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.