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Almost Automorphic Integrals of Almost Automorphic Functions

Published online by Cambridge University Press:  20 November 2018

M. Zaki
M. Zaki*
Affiliation:
Sir George Williams University, Montreal, Quebec
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Bochner has introduced the idea of almost automorphy in various contexts (see for example [1] and [2]). We shall use the following definition:

A measurable real valued function f of a real variable will be called almost automorphic if from every given infinite sequence of real numbers we can extract a subsequence {αn} such that

  • (i) exits for every real t but no kind of uniformity of convergence is stipulated;

  • (ii) exits for every t;

  • (iii) for every t.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 3 , September 1972 , pp. 433 - 436
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Bochner, S.,Continuous mappings of almost automorphic and almost periodic functions, Proc. Nat. Acad. Sci. U.S.A., 52, 1964, 907-910.Google Scholar
2. Bochner, S., Uniform convergence of monotone sequences of functions, Proc. Nat. Acad. Sci. U.S.A., 47 (1961), 582-585.Google Scholar