Next Article in Journal
Construction of Periodic Wavelet Frames Generated by the Walsh Polynomials
Next Article in Special Issue
Two Dimensional Temperature Distributions in Plate Heat Exchangers: An Analytical Approach
Previous Article in Journal
The San Francisco MSM Epidemic: A Retrospective Analysis
Previous Article in Special Issue
Gauge Invariance and Symmetry Breaking by Topology and Energy Gap
Open AccessArticle

Free W*-Dynamical Systems From p-Adic Number Fields and the Euler Totient Function

1
Department of Mathematics, St. Ambrose University, 421 Ambrose Hall, 518 W. Locust St., Davenport, IA 52803, USA
2
Department of Mathematics, University of Iowa, 14 McLean Hall, Iowa City, IA 52242, USA
*
Authors to whom correspondence should be addressed.
Academic Editor: Lokenath Debnath
Mathematics 2015, 3(4), 1095-1138; https://doi.org/10.3390/math3041095
Received: 26 May 2015 / Revised: 18 September 2015 / Accepted: 23 September 2015 / Published: 2 December 2015
(This article belongs to the Special Issue Mathematical physics)
In this paper, we study relations between free probability on crossed product W * -algebras with a von Neumann algebra over p-adic number fields ℚp (for primes p), and free probability on the subalgebra Φ, generated by the Euler totient function ϕ, of the arithmetic algebra A , consisting of all arithmetic functions. In particular, we apply such free probability to consider operator-theoretic and operator-algebraic properties of W * -dynamical systems induced by ℚp under free-probabilistic (and hence, spectral-theoretic) techniques. View Full-Text
Keywords: p-Adic number fields ℚp; p-Adic von neumann algebras ℳp; dynamical systems induced by ℚp; arithmetic functions; the arithmetic algebra A; the euler totient function ϕ p-Adic number fields ℚp; p-Adic von neumann algebras ℳp; dynamical systems induced by ℚp; arithmetic functions; the arithmetic algebra A; the euler totient function ϕ
MDPI and ACS Style

Cho, I.; Jorgensen, P.E.T. Free W*-Dynamical Systems From p-Adic Number Fields and the Euler Totient Function. Mathematics 2015, 3, 1095-1138.

Show more citation formats Show less citations formats

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop