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Chromatic Expansions and the Bargmann Transform

  • Ahmed I. ZayedEmail author
Chapter
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Abstract

Chromatic series expansions of bandlimited functions have recently been introduced in signal processing with promising results. Chromatic series share similar properties with Taylor series insofar as the coefficients of the expansions, which are called chromatic derivatives, are based on the ordinary derivatives of the function, but unlike Taylor series, chromatic series have more practical applications.The Bargmann transform was introduced in 1961 by V. Bargmann who showed, among other things, that the Bargmann transform is a unitary transformation from L 2(I​​R n ) onto the Bargmann–Segal–Foch space \(\mathfrak{F}\) on which Foch’s operator solutions to some equations in quantum mechanics are realized.The goal of this article is to survey results on chromatic derivatives and explore the connection between chromatic derivatives and series on the one hand and the Bargmann transform and the Bargmann–Segal–Foch space on the other hand.

Keywords

Bargmann Transform Chromene Derivatives Serum Chromium Band-limited Functions Normalized Hermite Functions 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer New York 2013

Authors and Affiliations

  1. 1.Department of Mathematical SciencesDePaul UniversityChicagoUSA

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