Generalized Hermite expansions of functions arising from Hardy conditions

Generalized Hermite expansions of functions arising from Hardy conditions

Consider a function on ℝ which is -finite. Assume that both and its Dunkl Fourier transform are bounded by for some . We will show that the generalized Hermite coefficients of will have exponential decay.

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Bibliographische Detailangaben
Veröffentlicht in:Advances in pure and applied mathematics (Berlin, Germany) Germany), 2013-04, Vol.4 (1), p.67-91
1. Verfasser: Parui, Sanjay
Format: Artikel
Sprache:eng
Schlagworte:
Dunkl transform
Fourier transforms
Uncertainty principles
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Beschreibung
Zusammenfassung:Consider a function on ℝ which is -finite. Assume that both and its Dunkl Fourier transform are bounded by for some . We will show that the generalized Hermite coefficients of will have exponential decay.
ISSN:1867-1152
1869-6090
DOI:10.1515/apam-2013-0205