A Uniqueness Theorem for Functions with Positive Imaginary Part

1971 ◽  
pp. 107-112
Author(s):  
B. S. Pavlov
Keyword(s):  
Uniqueness Theorem ◽  
Imaginary Part ◽  
Positive Imaginary Part

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

Upper bounds of some special zeros for the Rankin-Selberg L-function

2020 ◽  
Vol 70 (4) ◽  
pp. 795-806
Author(s):  
Kajtaz H. Bllaca
Keyword(s):  
Imaginary Part ◽  
Upper Bound ◽  
Upper Bounds ◽  
Central Point ◽  
Positive Imaginary Part

AbstractIn this paper, we prove some conditional results about the order of zero at central point s = 1/2 of the Rankin-Selberg L-function L(s, πf × π͠′f). Then, we give an upper bound for the height of the first zero with positive imaginary part of L(s, πf × π͠′f). We apply our results to automorphic L-functions.

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