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Paper Information

Journal:   BANACH JOURNAL OF MATHEMATICAL ANALYSIS   2017 , Volume 11 , Number 1; Page(s) 50 To 71.
 
Paper: 

ABSTRACT HARMONIC ANALYSIS OF WAVE-PACKET TRANSFORMS OVER LOCALLY COMPACT ABELIAN GROUPS

 
 
Author(s):  GHAANI FARASHAHI ARASH*
 
* 
 
Abstract: 

This article presents a systematic study for abstract harmonic analysis aspects of wave-packet transforms over locally compact abelian (LCA) groups. Let HH be a locally compact group, let KK be an LCA group, and let q:H®Aut(K) q:H®Aut(K) be a continuous homomorphism. We introduce the abstract notion of the wave-packet group generated by q, and we study basic properties of wave-packet groups. Then we study theoretical aspects of wave-packet transforms. Finally, we will illustrate application of these techniques in the case of some well-known examples.

 
Keyword(s): COHERENT STATE (COVARIANT) TRANSFORM, WAVE-PACKET GROUP, WAVE-PACKET REPRESENTATION, WAVE-PACKET TRANSFORM, WAVELET (GABOR) TRANSFORM
 
References: 
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