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

  • Doron Zeilberger (a1)
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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.

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References
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Ferrand, J. (1944). ‘Fonctions pre'harmonique et fonctions pre'holomorphees’. Bull. Sci. Math. 68, 152180.
Duffin, R. J. (1956), ‘Basic properties of discrete analytic functions’. Duke Math. J. 23, 335363.
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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