## 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

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## 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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ICMJE

MLA

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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.3160410203Daubechies, 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.

## 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