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A discrete analogue of the Paley-Wiener theorem for bounded analytic functions in a half plane

Published online by Cambridge University Press:  09 April 2009

Doron Zeilberger
Affiliation:
Department of Mathematics, The Weizmann Institute of Science, Rehovot, Israel.
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In this note we prove a discrete analogue to the following Paley–Weiner theorem: Let f be the restriction to the line of a bounded analytic function in the upper half plane; then the spectrum of f is contained in ([0, ∈). The discrete analogue of complex analysis is the theory of discrete analytic functions invented by Lelong-Ferrand (1944) and developed by Duffin (1956) and others.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1977

References

Ferrand, J. (1944). ‘Fonctions pre'harmonique et fonctions pre'holomorphees’. Bull. Sci. Math. 68, 152180.Google Scholar
Duffin, R. J. (1956), ‘Basic properties of discrete analytic functions’. Duke Math. J. 23, 335363.CrossRefGoogle Scholar