Math @ Duke

Publications [#318290] of Ingrid Daubechies
Papers Published
 Daubechies, I; Grossmann, A, Frames in the bargmann space of entire functions,
Communications on Pure and Applied Mathematics, vol. 41 no. 2
(January, 1988),
pp. 151164, WILEY [doi]
(last updated on 2019/09/24)
Abstract: 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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