Journal article
Markov measures and extended zeta functions
Journal of Applied Mathematics and Computing, Vol.38(1), pp.305-323
02/2012
DOI: 10.1007/s12190-011-0480-5
Abstract
In this paper we study a family of representations of the Cuntz algebras O p where p is a prime. These algebras are built on generators and relations. They are C ∗-algebras and their representations are a part of non-commutative harmonic analysis. Starting with specific generators and relations we pass to an ambient C ∗-algebra, for example in one of the Cuntz-algebras. Our representations are motivated by the study of frequency bands in signal processing: We construct induced measures attached to those representations which turned out to be related to a class of zeta functions. For a particular case those measures give rise to a class of Markov measures and q-Bernoulli polynomials. Our approach is amenable to applications in problems from dynamics and mathematical physics: We introduce a deformation parameter q, and an associated family of q-relations where the number q is a “quantum-deformation,” and also a parameter in a scale of (Riemann-Ruelle) zeta functions. Our representations are used in turn in a derivation of formulas for this q-zeta function.
Details
- Title: Subtitle
- Markov measures and extended zeta functions
- Creators
- P Jorgensen - Department of Mathematics University of Iowa Iowa City IA 52224 USAA Paolucci - Max-Planck-Institut für Mathematik Vivatsgasse 7 53111 Bonn Germany
- Resource Type
- Journal article
- Publication Details
- Journal of Applied Mathematics and Computing, Vol.38(1), pp.305-323
- Publisher
- Springer-Verlag; Berlin/Heidelberg
- DOI
- 10.1007/s12190-011-0480-5
- ISSN
- 1598-5865
- eISSN
- 1865-2085
- Language
- English
- Date published
- 02/2012
- Academic Unit
- Mathematics
- Record Identifier
- 9983985991602771
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