Sets of uniqueness for trigonometric series and integrals
1950 ◽
Vol 46
(4)
◽
pp. 538-548
◽
Keyword(s):
It is well known that, if a trigonometric seriesconverges to zero in 0 ≤ x < 2π then all the coefficients are zero. To generalize this property of the series, sets of uniqueness have been defined. A point-set E in 0 ≤ x < 2π is a set of uniqueness if every series (0·1), converging to zero in [0, 2π) − E, has zero coefficients. Otherwise E is a set of multiplicity. For example, every enumerable set is a set of uniqueness. An account of the theory may be found in Zygmund (2), chapter 11, pp. 267 et seq.
1982 ◽
Vol 34
(3)
◽
pp. 759-764
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Keyword(s):
1978 ◽
Vol 21
(2)
◽
pp. 149-158
◽
1979 ◽
Vol 31
(4)
◽
pp. 858-866
◽
Keyword(s):
1973 ◽
Vol 74
(1)
◽
pp. 107-116
◽
Keyword(s):
1968 ◽
Vol 9
(1)
◽
pp. 30-35
◽
1989 ◽
Vol 41
(3)
◽
pp. 508-555
◽
Keyword(s):
1931 ◽
Vol 27
(2)
◽
pp. 163-173
Keyword(s):
2002 ◽
Vol 193
(4)
◽
pp. 609-633
◽
1994 ◽
Vol 49
(2)
◽
pp. 333-339
◽
Keyword(s):