Wavelets in Banach Spaces

Details Wavelets in Banach Spaces Wavelets in Banach Spaces

1998-07-25

arxiv.org/abs/math/9807141v3

Acta Appl. Math. 59(1999), no. 1, pp. 79--109

Mathematics

Functional Analysis

37 pages; LaTeX2e; no pictures; 27/07/99: many small corrections

Scientific paper

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.

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