On the singular spectrum of the friedrichs model operators in a neighborhood of a singular point

1998 ◽  
Vol 32 (3) ◽  
pp. 214-217
Author(s):  
S. I. Yakovlev
Keyword(s):  
Singular Point ◽  
Singular Spectrum ◽  
Friedrichs Model

scholarly journals Description of the structure of singular spectrum for Friedrichs model operator near singular point

2001 ◽  
Vol 28 (1) ◽  
pp. 25-40
Author(s):  
Serguei I. Iakovlev
Keyword(s):  
Analytic Function ◽  
Singular Point ◽  
Uniqueness Theorem ◽  
Analytic Functions ◽  
Point Spectrum ◽  
Positive Imaginary Part ◽  
Model Operator ◽  
Real Roots ◽  
Singular Spectrum ◽  
Friedrichs Model

The study of the point spectrum and the singular continuous one is reduced to investigating the structure of the real roots set of an analytic function with positive imaginary partM(λ). We prove a uniqueness theorem for such a class of analytic functions. Combining this theorem with a lemma on smoothness ofM(λ)near its real roots permits us to describe the density of the singular spectrum.

scholarly journals Examples of Friedrichs model operators with a cluster point of eigenvalues

2003 ◽  
Vol 2003 (10) ◽  
pp. 625-638 ◽  
Author(s):  
Serguei I. Iakovlev
Keyword(s):  
Singular Point ◽  
Modulus Of Continuity ◽  
Finiteness Condition ◽  
Cluster Point ◽  
Selfadjoint Operators ◽  
Singular Spectrum ◽  
Friedrichs Model

A family of selfadjoint operators of the Friedrichs model is considered. These symmetric type operators have one singular point, zero of orderm. For everym>3/2, we construct a rank 1 perturbation from the classLip1such that the corresponding operator has a sequence of eigenvalues converging to zero. Thus, near the singular point, there is no singular spectrum finiteness condition in terms of a modulus of continuity of a perturbation for these operators in case ofm>3/2.

First order over determined system with singular point

2007 ◽  
Vol 18 (1) ◽  
pp. 65-80
Author(s):  
Adel Nasim Adib ◽  
Nusrat Rajabov
Keyword(s):  
Singular Point ◽  
First Order

Boundary Value Problems of Electroelasticity with Concentrated Singularities

1994 ◽  
Vol 1 (5) ◽  
pp. 459-467
Author(s):  
T. Buchukuri ◽  
D. Yanakidi
Keyword(s):  
Singular Point ◽  
Boundary Value Problems ◽  
Power Function ◽  
Boundary Value ◽  
Linearly Independent

Abstract We investigate the solutions of boundary value problems of linear electroelasticity, having growth as a power function in the neighbourhood of infinity or in the neighbourhood of an isolated singular point. The number of linearly independent solutions of this type is established for homogeneous boundary value problems.

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