Markov measures and extended zeta functions

作     者：Jorgensen, P. E. T. Paolucci, A. M. 

作者机构：Univ Iowa Dept Math Iowa City IA 52224 USA Max Planck Inst Math D-53111 Bonn Germany 

出 版 物：《JOURNAL OF APPLIED MATHEMATICS AND COMPUTING》 (国际应用数学与计算杂志)

年 卷 期：2012年第38卷第1-2期

页      面：305-323页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Science Foundation (USA) 

主　　题：Commutator Quantum theory Signal processing Zeta functions Hilbert space Spectrum 

摘      要：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.