Analysis on locally compact abelian groups and local fields has applications in a variety of different fields. Traditional Fourier analysis is based on the characters of Rⁿ, Tⁿ, and Zⁿ. There is a growing body of literature using functions on ρ-adic groups to model quantum phenomena, and ρ-adic wavelets diagonalize certain important pseudo-differential operators. Fourier analysis on local fields comes up in class field theory and in the study of particular zeta functions. This paper will present known results in the field and future directions of research.

Date Published: 26 September 2013
PDF: 10 pages
Proc. SPIE 8858, Wavelets and Sparsity XV, 88581R (26 September 2013); doi: 10.1117/12.2025018

Published in SPIE Proceedings Vol. 8858:
Wavelets and Sparsity XV
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)