LIEB–THIRRING TYPE ESTIMATES FOR DIRICHLET LAPLACIANS ON SPIRAL-SHAPED DOMAINS

IF 1.2 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
JUAN BORY-REYES , DIANA BARSEGHYAN, BARUCH SCHNEIDER
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引用次数: 0

Abstract

In this present paper we consider the asymptotically Archimedean spiral-shaped regions for which the Dirichlet Laplacian spectrum consists of the essential part and the eigenvalues below the threshold of the essential spectrum. Our purpose here is to obtain the bounds on the moments of these eigenvalues in terms of the geometric properties of the region. As a consequence of the mentioned bound we describe the class of the asymptotically Archimedean spiral-shaped regions such that the Dirichlet Laplacian has only a finite number of eigenvalues below the threshold of the essential spectrum.
螺旋形区域上狄利克雷拉普拉斯算子的Lieb-thirring型估计
本文考虑了狄利克雷拉普拉斯谱由本质部分和低于本质谱阈值的特征值组成的渐近阿基米德螺旋形区域。我们的目的是根据区域的几何性质得到这些特征值的矩的边界。作为上述界的结果,我们描述了一类渐近阿基米德螺旋形区域,使得狄利克雷拉普拉斯函数只有有限数量的特征值低于本质谱的阈值。
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来源期刊
Reports on Mathematical Physics
Reports on Mathematical Physics 物理-物理:数学物理
CiteScore
1.80
自引率
0.00%
发文量
40
审稿时长
6 months
期刊介绍: Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
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