Frame theory for locally compact abelian groups

Emily J. King

doi:10.1117/12.2025018

26 September 2013 Frame theory for locally compact abelian groups

Emily J. King

Proceedings Volume 8858, Wavelets and Sparsity XV; 88581R (2013) https://doi.org/10.1117/12.2025018
Event: SPIE Optical Engineering + Applications, 2013, San Diego, California, United States

Abstract

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.

Citation Download Citation

Emily J. King "Frame theory for locally compact abelian groups", Proc. SPIE 8858, Wavelets and Sparsity XV, 88581R (26 September 2013); https://doi.org/10.1117/12.2025018

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