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Entire Mean Periodic Functions

Published online by Cambridge University Press:  20 November 2018

P. G. Laird
P. G. Laird*
Affiliation:
The University of Wollongong, Wollongong, N.S.W. 2500, A ustralia
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Let H denote the set of all entire functions of a single complex variable equipped with the topology of convergence uniform on all compact subsets of C, the set of complex numbers. Then an entire function f is mean periodic if the subspace spanned by f and its complex translates is not dense in H. It was shown by Schwartz [13, p. 922] in 1947, to whom this definition is due, that any such function is the limit in H of a certain sequence of exponential polynomials.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 4 , 01 August 1975 , pp. 805 - 818
Copyright
Copyright © Canadian Mathematical Society 1975

References

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