Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (2): 807-812.doi: 10.1016/S0252-9602(12)60061-7

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CONTINUOUS FRAME WAVELETS

Ali Akbar Arefijamaal|Narguess Tavallaei   

  1. Department of Mathematics and Computer Science, Sabzevar Tarbiat Moallem University, Sabzevar, Iran; Department of Pure Mathematics, School of Mathematics and Computer Science, Damghan University, Damghan, Iran
  • Received:2010-01-12 Revised:2011-02-24 Online:2012-03-20 Published:2012-03-20

Abstract:

Let π be a unitary representation of a locally compact topological group G on a separable Hilbert space H. A vector ΨH is called a continuous frame wavelet if there exist A, B > 0 such that
A||Φ||2 ≤∫G|<π(g)Ψ ,Φ|2dgB||Φ|| (ΦH),

in which dg is the left Haar measure of G. Similar to the study of wavelets, an essential problem in the study of continuous frame wavelets is how to characterize them under the given unitary representation. Moreover, we investigate a relation between admissible vectors of π and its components.

Key words: Locally compact group, unitary representation, continuous frame, wavelet transform, direct integral

CLC Number: 

  • 43A65
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