scholarly journals Uniqueness theorems for operator-valued functions with positive imaginary part, and the singular spectrum in the selfadjoint Friedrichs model

1987 ◽  
Vol 25 (1-2) ◽  
pp. 115-140 ◽  
Author(s):  
S. N. Naboko
Keyword(s):  
Imaginary Part ◽  
Uniqueness Theorems ◽  
Positive Imaginary Part ◽  
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.

3.4. Null-sets of operator functions with a positive imaginary part

1984 ◽  
Vol 26 (5) ◽  
pp. 2144-2146 ◽  
Author(s):  
B. S. Pavlov ◽  
L. D. Faddeev
Keyword(s):  
Imaginary Part ◽  
Positive Imaginary Part ◽  
Operator Functions
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