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Frames in the bargmann space of entire functions

Publication ,  Journal Article
Daubechies, I; Grossmann, A
Published in: Communications on Pure and Applied Mathematics
January 1, 1988

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

Duke Scholars

Published In

Communications on Pure and Applied Mathematics

DOI

EISSN

1097-0312

ISSN

0010-3640

Publication Date

January 1, 1988

Volume

41

Issue

2

Start / End Page

151 / 164

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Daubechies, I., & Grossmann, A. (1988). Frames in the bargmann space of entire functions. Communications on Pure and Applied Mathematics, 41(2), 151–164. https://doi.org/10.1002/cpa.3160410203
Daubechies, I., and A. Grossmann. “Frames in the bargmann space of entire functions.” Communications on Pure and Applied Mathematics 41, no. 2 (January 1, 1988): 151–64. https://doi.org/10.1002/cpa.3160410203.
Daubechies I, Grossmann A. Frames in the bargmann space of entire functions. Communications on Pure and Applied Mathematics. 1988 Jan 1;41(2):151–64.
Daubechies, I., and A. Grossmann. “Frames in the bargmann space of entire functions.” Communications on Pure and Applied Mathematics, vol. 41, no. 2, Jan. 1988, pp. 151–64. Scopus, doi:10.1002/cpa.3160410203.
Daubechies I, Grossmann A. Frames in the bargmann space of entire functions. Communications on Pure and Applied Mathematics. 1988 Jan 1;41(2):151–164.
Journal cover image

Published In

Communications on Pure and Applied Mathematics

DOI

EISSN

1097-0312

ISSN

0010-3640

Publication Date

January 1, 1988

Volume

41

Issue

2

Start / End Page

151 / 164

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics