A class of sets of uniqueness for multiple Walsh series

2009 ◽  
Vol 64 (2) ◽  
pp. 55-61 ◽  
Author(s):  
T. A. Zhereb’eva
Keyword(s):  
Walsh Series ◽  
Sets Of Uniqueness ◽  
Multiple Walsh Series

Multiple walsh series and Zygmund sets

2014 ◽  
Vol 95 (5-6) ◽  
pp. 686-696 ◽  
Author(s):  
M. G. Plotnikov
Keyword(s):  
Walsh Series ◽  
Multiple Walsh Series

Perfect Sets of Uniqueness on the Group 2ω

1982 ◽  
Vol 34 (3) ◽  
pp. 759-764 ◽  
Author(s):  
Kaoru Yoneda
Keyword(s):  
Haar Measure ◽  
Measure Zero ◽  
Countable Subset ◽  
Walsh Series ◽  
Dyadic Group ◽  
Set Of Uniqueness ◽  
Image Position ◽  
Sets Of Uniqueness

Let ω0, ω1, … denote the Walsh-Paley functions and let G denote the dyadic group introduced by Fine [3]. Recall that a subset E of G is said to be a set of uniqueness if the zero series is the only Walsh series ∑ akωk which satisfiesA subset E of G which is not a set of uniqueness is called a set of multiplicity.It is known that any subset of G of positive Haar measure is a set of multiplicity [5] and that any countable subset of G is a set of uniqueness [2]. As far as uncountable subsets of Haar measure zero are concerned, both possibilities present themselves. Indeed, among perfect subsets of G of Haar measure zero there are sets of multiplicity [1] and there are sets of uniqueness [5].

On uniqueness sets for multiple Walsh series

2007 ◽  
Vol 81 (1-2) ◽  
pp. 234-246 ◽  
Author(s):  
M. G. Plotnikov
Keyword(s):  
Walsh Series ◽  
Uniqueness Sets ◽  
Multiple Walsh Series
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