Asymptotic and spectral analysis of non-selfadjoint operators generated by a filament model with a critical value of a boundary parameter

2003 ◽  
Vol 26 (3) ◽  
pp. 213-245 ◽  
Author(s):  
Marianna A. Shubov
Keyword(s):  
Spectral Analysis ◽  
Critical Value ◽  
Selfadjoint Operators ◽  
Boundary Parameter

scholarly journals Spectral Analysis of Schrödinger Operators with Unusual Semiclassical Behavior

10.14311/1801 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Pavel Exner ◽  
Diana Barseghyan
Keyword(s):  
Spectral Analysis ◽  
Phase Space ◽  
Lower Bounds ◽  
Dirichlet Boundary ◽  
Schrödinger Operators ◽  
Critical Value ◽  
Upper And Lower Bounds ◽  
Schrodinger Operators ◽  
Two Dimensional ◽  
Eigenvalue Bounds

In this paper we discuss several examples of Schrödinger operators describing a particle confined to a region with thin cusp-shaped ‘channels’, given either by a potential or by a Dirichlet boundary; we focus on cases when the allowed phase space is infinite but the operator still has a discrete spectrum. First we analyze two-dimensional operators with the potential |xy|p - ?(x2 + y2)p/(p+2)where p?1 and ??0. We show that there is a critical value of ? such that the spectrum for ??crit it is unbounded from below. In the subcriticalcase we prove upper and lower bounds for the eigenvalue sums. The second part of work is devoted toestimates of eigenvalue moments for Dirichlet Laplacians and Schrödinger operators in regions havinginfinite cusps which are geometrically nontrivial being either curved or twisted; we are going to showhow these geometric properties enter the eigenvalue bounds.

Spectral analysis of asymmetry training effect for depression

2008 ◽  
Author(s):  
Ji Ha Lee ◽  
Sung Won Choi ◽  
Ji Sun Min ◽  
Eun Ju Jaekal ◽  
Gyhye Sung
Keyword(s):  
Spectral Analysis ◽  
Training Effect
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