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Formal multiplication of trigonometric series

Published online by Cambridge University Press:  09 April 2009

Masako Izumi  and
Shin-Ichi Izumi
Masako Izumi
Affiliation:
Department of Mathematics Australian National University
Shin-Ichi Izumi
Affiliation:
Department of Mathematics Australian National University
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Let be the given trigonometric series, then the formal product of them is defined by where the last series is supposed to be convergent for every n.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 1 , August 1973 , pp. 70 - 77
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Zygmund, A., Trigonometric series, Chapter IX (Cambridge University Press, 1959).Google Scholar
[2]Zygmund, A., ‘A theorem on the formal multiplication of trigonometric series’, Functional Analysis and Related Fields (Proc. Conf, for M. Stone, Univ. Chicago, Chicago, Illinois, (1968), 224–227 Springer, New York, 1970).Google Scholar