Perfect Sets of Uniqueness on the Group 2ω
1982 ◽
Vol 34
(3)
◽
pp. 759-764
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Keyword(s):
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].
1979 ◽
Vol 31
(4)
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pp. 858-866
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Keyword(s):
1950 ◽
Vol 46
(4)
◽
pp. 538-548
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Keyword(s):
1958 ◽
Vol 11
(2)
◽
pp. 71-77
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1970 ◽
Vol 13
(4)
◽
pp. 497-499
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1979 ◽
Vol 31
(2)
◽
pp. 441-447
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Keyword(s):
1978 ◽
Vol 19
(1)
◽
pp. 49-56
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1957 ◽
Vol 53
(2)
◽
pp. 312-317
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Keyword(s):
1974 ◽
Vol 76
(1)
◽
pp. 173-181
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Keyword(s):
1987 ◽
Vol 39
(1)
◽
pp. 123-148
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Keyword(s):
1972 ◽
Vol 24
(5)
◽
pp. 957-966
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Keyword(s):