scholarly journals Approximation by crystal-refinable functions

2019 ◽  
Vol 207 (1) ◽  
pp. 1-21
Author(s):  
Ursula Molter ◽  
María del Carmen Moure ◽  
Alejandro Quintero
Keyword(s):  
Refinable Functions

Building refinable functions from their values at integers

CALCOLO ◽  
2000 ◽  
Vol 37 (3) ◽  
pp. 139-158 ◽  
Author(s):  
Johan M. de Villiers ◽  
Charles A. Micchelli ◽  
Thomas Sauer
Keyword(s):  
Refinable Functions

scholarly journals The regularity of refinable functions

2013 ◽  
Vol 34 (1) ◽  
pp. 142-147
Author(s):  
Yang Wang ◽  
Zhiqiang Xu
Keyword(s):  
Refinable Functions

Totally positive refinable functions with general dilation M

2017 ◽  
Vol 112 ◽  
pp. 17-26
Author(s):  
Laura Gori ◽  
Francesca Pitolli
Keyword(s):  
Refinable Functions ◽  
Totally Positive

scholarly journals Multiresolution analysis and wavelets on Vilenkin groups

2008 ◽  
Vol 21 (3) ◽  
pp. 309-325 ◽  
Author(s):  
Yury Farkov
Keyword(s):  
Multiresolution Analysis ◽  
Linear Independence ◽  
Sufficient Conditions ◽  
Partition Of Unity ◽  
Necessary And Sufficient Conditions ◽  
Refinable Functions ◽  
Vilenkin Groups ◽  
Orthogonal Wavelets ◽  
The Stability ◽  
Necessary And Sufficient

This paper gives a review of multiresolution analysis and compactly sup- ported orthogonal wavelets on Vilenkin groups. The Strang-Fix condition, the partition of unity property, the linear independence, the stability, and the orthonormality of 'integer shifts' of the corresponding refinable functions are considered. Necessary and sufficient conditions are given for refinable functions to generate a multiresolution analysis in the L2-spaces on Vilenkin groups. Several examples are provided to illustrate these results. .

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