A fractal set constructed from a class of wavelet sets

2002 ◽  
pp. 19-35 ◽  
Author(s):  
John J. Benedetto ◽  
Songkiat Sumetkijakan
Keyword(s):  
Wavelet Sets ◽  
Fractal Set

Scaling sets and generalized scaling sets on Cantor dyadic group

2020 ◽  
Vol 18 (04) ◽  
pp. 2050019
Author(s):  
Prasadini Mahapatra ◽  
Divya Singh
Keyword(s):  
Abelian Groups ◽  
Real Case ◽  
Locally Compact ◽  
Wavelet Sets ◽  
Locally Compact Abelian Groups ◽  
Dyadic Group ◽  
Compact Abelian Groups ◽  
Cantor Dyadic Group

Scaling and generalized scaling sets determine wavelet sets and hence wavelets. In real case, wavelet sets were proved to be an important tool for the construction of MRA as well as non-MRA wavelets. However, any result related to scaling/generalized scaling sets is not available in case of locally compact abelian groups. This paper gives a characterization of scaling sets and its generalized version along with relevant examples in dual Cantor dyadic group [Formula: see text]. These results can further be generalized to arbitrary locally compact abelian groups.

scholarly journals Frame wavelet sets in $\mathbb {R}$

2000 ◽  
Vol 129 (7) ◽  
pp. 2045-2055 ◽  
Author(s):  
X. Dai ◽  
Y. Diao ◽  
Q. Gu
Keyword(s):  
Wavelet Sets

scholarly journals Frame wavelet sets in Rd

2003 ◽  
Vol 155 (1) ◽  
pp. 69-82 ◽  
Author(s):  
X. Dai ◽  
Y. Diao ◽  
Q. Gu ◽  
D. Han
Keyword(s):  
Wavelet Sets

scholarly journals Derivatives not first return integrable on a fractal set

2018 ◽  
Vol 67 (2) ◽  
pp. 597-604
Author(s):  
Donatella Bongiorno
Keyword(s):  
Fractal Set
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