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A sequence algebra associated with distributions

Published online by Cambridge University Press:  17 April 2009

G.M. Petersen
G.M. Petersen
Affiliation:
Department of Mathematics, University of Canterbury, Christchurch, New Zealand.
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Abstract

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If A = {am,n} is a regular summability matrix, the sequence s = {sn} is said to be A uniformly distributed (see L. Kuipers, H. Niederreiter, Uniform distribution of sequences, p. 221, John Wiley & Sons, New York, London, Sydney, Toronto, 1974), if

(h = 1, 2, …). In this paper we examine sequences belonging to A*, where t ∈ A* if and only if t is bounded and s + t is A uniformly distributed whenever s is A uniformly distributed. By A′ are denoted those members t of A* such that at ∈ A* for every real a. The members of A′ form a Banach algebra, A* is not connected under the sup norm, but A′ is a component.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 1 , August 1978 , pp. 39 - 49
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Kuipers, L., Niederreiter, H., Uniform distribution of sequences (John Wiley & Sons, New York, London, Sydney, 1974).Google Scholar
[2]Petersen, Gordon M., “Factor sequences for summability matrices”, Math. Z. 112 (1969), 389–392.CrossRefGoogle Scholar
[3]Petersen, G.M., “Factor sequences and their algebras”, Jber. Deutsch. Math.-Verein. 74 (1972/1973), 182–188.Google Scholar
[4]Petersen, G.M. and Zame, A., “Summability properties for the distribution of sequences”, Monatsh. Math. 73 (1969), 147–158.CrossRefGoogle Scholar