Factorization Versus Invertibility of Matrix Functions on Compact Abelian Groups

2012 ◽  
pp. 225-239
Author(s):  
Alex Brudnyi ◽  
Leiba Rodman ◽  
Ilya M. Spitkovsky
Keyword(s):  
Abelian Groups ◽  
Matrix Functions ◽  
Compact Abelian Groups

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.

Singular measures with absolutely continuous convolution squares

1966 ◽  
Vol 62 (3) ◽  
pp. 399-420 ◽  
Author(s):  
Edwin Hewitt ◽  
Herbert S. Zuckerman
Keyword(s):  
Abelian Groups ◽  
Natural Order ◽  
Continuous Measure ◽  
Locally Compact ◽  
Absolutely Continuous ◽  
Character Group ◽  
Locally Compact Abelian Groups ◽  
Singular Measures ◽  
Compact Abelian Groups ◽  
Nikodym Derivative

Introduction. A famous construction of Wiener and Wintner ((13)), later refined by Salem ((11)) and extended by Schaeffer ((12)) and Ivašev-Musatov ((8)), produces a non-negative, singular, continuous measure μ on [ − π,π[ such thatfor every ∈ > 0. It is plain that the convolution μ * μ is absolutely continuous and in fact has Lebesgue–Radon–Nikodým derivative f such that For general locally compact Abelian groups, no exact analogue of (1 · 1) seems possible, as the character group may admit no natural order. However, it makes good sense to ask if μ* μ is absolutely continuous and has pth power integrable derivative. We will construct continuous singular measures μ on all non-discrete locally compact Abelian groups G such that μ * μ is a absolutely continuous and for which the Lebesgue–Radon–Nikodým derivative of μ * μ is in, for all real p > 1.

Extensions of the Golden hypergroup by locally compact Abelian groups

2012 ◽  
Vol 78 (1-2) ◽  
pp. 351-368
Author(s):  
Satoshi Kawakami ◽  
Satoe Yamanaka
Keyword(s):  
Abelian Groups ◽  
Locally Compact ◽  
Locally Compact Abelian Groups ◽  
Compact Abelian Groups

scholarly journals Densities on locally compact abelian groups

1969 ◽  
Vol 19 (1) ◽  
pp. 81-107 ◽  
Author(s):  
I. D. Berg ◽  
L. A. Rubel
Keyword(s):  
Abelian Groups ◽  
Locally Compact ◽  
Locally Compact Abelian Groups ◽  
Compact Abelian Groups
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