Book chapter
A Harmonic Analysis of Directed Graphs from Arithmetic Functions and Primes
Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science, pp.603-651
Applied and Numerical Harmonic Analysis, Springer International Publishing
08/11/2017
DOI: 10.1007/978-3-319-55556-0_7
Abstract
In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By fixing a prime p and a graph G, we establish a noncommutative free probabilistic structure embedded in the algebra of all arithmetic functions. We act the additive group (ℝ,+),\documentclass[12pt]{minimal}
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$$(\mathbb{R},+),$$
\end{document} the flow, on the free probability space dependent both on p and on G, and construct uncountable families of free probability spaces determined by the flow. We study fundamental properties of such a family.
Details
- Title: Subtitle
- A Harmonic Analysis of Directed Graphs from Arithmetic Functions and Primes
- Creators
- Ilwoo Cho - Saint Ambrose UniversityPalle E. T Jorgensen - University of Iowa
- Resource Type
- Book chapter
- Publication Details
- Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science, pp.603-651
- Publisher
- Springer International Publishing; Cham
- Series
- Applied and Numerical Harmonic Analysis
- DOI
- 10.1007/978-3-319-55556-0_7
- eISSN
- 2296-5017
- ISSN
- 2296-5009
- Language
- English
- Date published
- 08/11/2017
- Academic Unit
- Mathematics
- Record Identifier
- 9984240867502771
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