v形波导中的分数阶拉普拉斯算子

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2024-11-14 DOI:10.1002/mana.202400271

Fedor Bakharev, Sergey Matveenko

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引用次数: 0

摘要

研究了v形波导中受限分数阶狄利克雷拉普拉斯算子的谱性质。已知具有圆柱形出口的域的连续谱占用射线[Λ†，+∞)$[\Lambda _\dagger, +\infty)$，其阈值对应于截面问题的最小特征值。在这项工作中，建立了在任何结角处离散谱的存在以及离散谱对该角的单调依赖性。

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Fractional Laplacian in V-shaped waveguide

The spectral properties of the restricted fractional Dirichlet Laplacian in V-shaped waveguides are studied. The continuous spectrum for such domains with cylindrical outlets is known to occupy the ray $[Λ_{†}, + \infty)$ with the threshold corresponding to the smallest eigenvalue of the cross-sectional problems. In this work, the presence of a discrete spectrum at any junction angle is established along with the monotonic dependence of the discrete spectrum on the angle.

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index