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Frames in the bargmann space of entire functions
Author(s) -
Daubechies Ingrid,
Grossmann A.
Publication year - 1988
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160410203
Subject(s) - mathematics , conjecture , hilbert space , space (punctuation) , integer (computer science) , entire function , decomposition , pure mathematics , combinatorics , ecology , philosophy , linguistics , computer science , biology , programming language
We look at the decomposition of arbitrary f in L 2 ( R ) in terms of the family of functions φ mn ( x ) = π −1/4 exp{ − 1/2 imnab + 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 formWe conjecture that these inequalities remain true for all a, b such that ab < 2π.