Frames in the bargmann space of entire functions

Journal Article (Journal Article)

We look at the decomposition of arbitrary f in L2(R) in terms of the family of functions φmn(x) = π−1/4exp{ − 1/2imnab + i max − 1/2(x − nb)2}, with a, b > 0. We derive bounds and explicit formulas for the minimal expansion coefficients in the case where ab = 2π/N, N an integer ≧ 2. Transported to the Hilbert space F of entire functions introduced by V. Bargmann, these results are expressed as inequalities of the form We conjecture that these inequalities remain true for all a, b such that ab < 2π. Copyright © 1988 Wiley Periodicals, Inc., A Wiley Company

Full Text

Duke Authors

Cited Authors

  • Daubechies, I; Grossmann, A

Published Date

  • January 1, 1988

Published In

Volume / Issue

  • 41 / 2

Start / End Page

  • 151 - 164

Electronic International Standard Serial Number (EISSN)

  • 1097-0312

International Standard Serial Number (ISSN)

  • 0010-3640

Digital Object Identifier (DOI)

  • 10.1002/cpa.3160410203

Citation Source

  • Scopus