scholarly journals Spectral theory, dynamics, and Selberg’s zeta function for Kleinian groups

2001 ◽  
pp. 145-165 ◽  
Author(s):  
Peter Perry
Keyword(s):  
Zeta Function ◽  
Spectral Theory ◽  
Kleinian Groups ◽  
Selberg’S Zeta Function

The divisor of Selberg's zeta function for Kleinian groups

2001 ◽  
Vol 106 (2) ◽  
pp. 321-390 ◽  
Author(s):  
S. J. Patterson ◽  
Peter A. Perry
Keyword(s):  
Zeta Function ◽  
Kleinian Groups ◽  
Selberg’S Zeta Function

scholarly journals Spectral Theory from the Second-Orderq-Difference Operator

2007 ◽  
Vol 2007 ◽  
pp. 1-14 ◽  
Author(s):  
Lazhar Dhaouadi
Keyword(s):  
Integral Representation ◽  
Zeta Function ◽  
Spectral Theory ◽  
Spectral Measure ◽  
Resolvent Operator ◽  
Difference Operator ◽  
Poincaré Inequality ◽  
Second Order ◽  
Poincare Inequality ◽  
The Resolvent Operator

Spectral theory from the second-orderq-difference operatorΔqis developed. We give an integral representation of its inverse, and the resolvent operator is obtained. As application, we give an analogue of the Poincare inequality. We introduce the Zeta function for the operatorΔqand we formulate some of its properties. In the end, we obtain the spectral measure.

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