Title : ( Some equivalent multiresolution conditions on locally compact abelian groups )
Authors: Rajab Ali Kamyabi Gol , Reihaneh Raisi Tousi ,
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Abstract
Conditions under which a function generates a multiresolution analysis are investigated. The definition of the spectral function of a shift invariant space is generalized from Rn to a locally compact abelian group and the union density and intersection triviality properties of a multiresolution analysis are characterized in terms of the spectral functions. Finally, all multiresolution analysis conditions are characterized in terms of the scaling and the spectral functions.
Keywords
Locally compact abelian group; multiresolution analysis; shift invariant space; spectral function; Parseval frame; range function.
@article{paperid:1018300,
author = {Kamyabi Gol, Rajab Ali and Raisi Tousi, Reihaneh},
title = {Some equivalent multiresolution conditions on locally compact abelian groups},
journal = {Proceedings of the Indian Academy of Sciences - Mathematical Sciences},
year = {2010},
volume = {120},
number = {3},
month = {June},
issn = {0253-4142},
pages = {317--331},
numpages = {14},
keywords = {Locally compact abelian group; multiresolution analysis; shift invariant
space; spectral function; Parseval frame; range function.},
}
%0 Journal Article
%T Some equivalent multiresolution conditions on locally compact abelian groups
%A Kamyabi Gol, Rajab Ali
%A Raisi Tousi, Reihaneh
%J Proceedings of the Indian Academy of Sciences - Mathematical Sciences
%@ 0253-4142
%D 2010
