Variational and Asymptotic Methods for Finding Eigenvalues below the Continuous Spectrum Threshold

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Variational and Asymptotic Methods for Finding Eigenvalues below the Continuous Spectrum Threshold

机译：寻找低于连续频谱阈值特征值的变分和渐近方法

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Considering the example of a mixed boundary value problem for the Helmholtz operator we discuss two methods for finding eigenvalues below the continuous spectrum threshold: one variational and the other-asymptotic. We construct asymptotics for the eigenvalue arising near the threshold as a small obstacle appears in the cylindrical waveguide. The resulting asymptotic formula, its derivation and justification differ substantially from the case of a bounded domain.

机译：考虑到Helmholtz算子的混合边值问题的示例，我们讨论了寻找低于连续频谱阈值的特征值的两种方法：一种是变分方法，另一种是渐近方法。当圆柱波导中出现小障碍物时，我们为渐近阈值的特征值构造渐近线。所得渐近公式，其派生和对正与有界域的情况大不相同。

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《Siberian Mathematical Journal》 |2010年第5期|共13页
作者
Nazarov SA;
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正文语种 eng
中图分类数学;
关键词
eigenvalue; discrete spectrum; waveguide; Helmholtz equation; trapped mode;

机译：特征值离散频谱波导Helmholtz方程陷波模;

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专利

1. Variational and Asymptotic Methods for Finding Eigenvalues below the Continuous Spectrum Threshold [J] . Nazarov SA Siberian Mathematical Journal . 2010,第5期

机译：寻找低于连续频谱阈值特征值的变分和渐近方法
2. Absence of eigenvalue at the bottom of the continuous spectrum on asymptotically hyperbolic manifolds [J] . Bouclet J.-M. Annals of global analysis and geometry . 2013,第2期

机译：渐近双曲型流形上连续谱底部的特征值不存在
3. Asymptotics of an Eigenvalue on the Continuous Spectrum of Two Quantum Waveguides Coupled through Narrow Windows [J] . S. A. Nazarov Mathematical notes . 2013,第1a2期

机译：通过窄窗耦合的两个量子波导连续谱上本征值的渐近性
4. Exact non-asymptotic threshold for eigenvalue-based spectrum sensing [C] . International Conference on Cognitive Radio Oriented Wireless Networks and Communications . 2009

机译：基于特征值的光谱感测的精确的非渐近阈值
5. EXTENSIONS, GENERALIZATIONS AND CLARIFICATIONS OF LOWER BOUND METHODS APPLIED TO EIGENVALUE PROBLEMS OF CONTINUOUS ELASTIC SYSTEMS. [D] . WELLS, LYNN TAYLOR. 1970

机译：适用于连续弹性系统特征值问题的下界方法的扩展，推广和澄清。
6. On the asymptotic eigenvalue distribution of a pseudo-differential operator [O] . C. Fefferman, D. H. Phong 1980

机译：伪微分算子的渐近特征值分布
7. Asymptotic formulas for trapped modes and for eigenvalues below the threshold of the continuous spectrum of a waveguide with a thin screening barrier [O] . S. A. Nazarov 2012

机译：被捕获模式的渐近公式，以及低于波导的连续谱的阈值，具有薄的筛选屏障的阈值
8. Energy Methods in Self-Adjoint Eigenvalue Problems. I. Variational Theory of the Spectrum [R] . Morduchow, M., Pulos, J. G. 1971

机译：自伴随特征值问题的能量方法。一，频谱的变分理论

Variational and Asymptotic Methods for Finding Eigenvalues below the Continuous Spectrum Threshold

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