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
APA
Chicago
ICMJE
MLA
NLM
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.
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