Wavelets in Banach Spaces
Functional Analysis
2007-05-23 v3 Mathematical Physics
Complex Variables
math.MP
Representation Theory
Quantum Physics
Abstract
We describe a construction of wavelets (coherent states) in Banach spaces generated by ``admissible'' group representations. Our main targets are applications in pure mathematics while connections with quantum mechanics are mentioned. As an example we consider operator valued Segal-Bargmann type spaces and the Weyl functional calculus. Keywords: Wavelets, coherent states, Banach spaces, group representations, covariant, contravariant (Wick) symbols, Heisenberg group, Segal-Bargmann spaces, Weyl functional calculus (quantization), second quantization, bosonic field.
Cite
@article{arxiv.math/9807141,
title = {Wavelets in Banach Spaces},
author = {Vladimir V. Kisil},
journal= {arXiv preprint arXiv:math/9807141},
year = {2007}
}
Comments
37 pages; LaTeX2e; no pictures; 27/07/99: many small corrections