On sets of uniqueness

1970 ◽  
pp. 203-217
Author(s):  
S. B. Stečkin ◽  
P. L. Ul′janov
Keyword(s):  
Sets Of Uniqueness

scholarly journals Sets of Uniqueness and Minimal Matrices

1998 ◽  
Vol 208 (2) ◽  
pp. 444-451 ◽  
Author(s):  
Adolfo Torres-Cházaro ◽  
Ernesto Vallejo
Keyword(s):  
Sets Of Uniqueness

A new type of sets of uniqueness

1988 ◽  
Vol 57 (2) ◽  
pp. 431-458 ◽  
Author(s):  
Russell Lyons
Keyword(s):  
New Type ◽  
Sets Of Uniqueness

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].

Algebraic Elements and Sets of Uniqueness in the Group of Integers of a p-Series Field

1986 ◽  
Vol 29 (2) ◽  
pp. 177-184 ◽  
Author(s):  
Bruce Aubertin
Keyword(s):  
Cantor Sets ◽  
Pisot Numbers ◽  
Algebraic Elements ◽  
Sets Of Uniqueness ◽  
Field Element

AbstractLet G be the group of integers of a p-series field. A class {E(θ)} of perfect null subsets of G is introduced and classified into M-sets and U-sets according to the arithmetical nature of the field element θ. This is analogous to the well-known classification, involving Pisot numbers, of certain Cantor sets on the circle.

Sets of Uniqueness for the Group of Integers of a p-Series Field

1979 ◽  
Vol 31 (4) ◽  
pp. 858-866 ◽  
Author(s):  
William R. Wade
Keyword(s):  
Dual Group ◽  
Negative Integer ◽  
Detailed Account ◽  
Basic Properties ◽  
Dyadic Group ◽  
Image Position ◽  
Sets Of Uniqueness ◽  
Prime 2

Let G denote the group of integers of a p-series field, where p is a prime ≦ 2. Thus, any element can be represented as a sequence {xi }i = 0∞ with 0 ≦ xi < p for each i ≦ 0. Moreover, the dual group {Ψm}m = 0∞ of G can be described by the following process. If m is a non-negative integer with for each k , and if then(1)where for each integer k ≧ 0 and for each x = {xi} ∈ G the functions Φk are defined by(2)In the case that p = 2, the group G is the dyadic group introduced by Fine [1] and the functions are the Walsh-Paley functions. A detailed account of these groups and basic properties can be found in [4].

scholarly journals Sets of uniqueness for functions regular in the unit circle

1952 ◽  
Vol 87 (0) ◽  
pp. 325-345 ◽  
Author(s):  
Lennart Carleson
Keyword(s):  
Unit Circle ◽  
Sets Of Uniqueness
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