Discrete analytic functions of exponential growth

Discrete analytic functions of exponential growth
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by Doron Zeilberger PDF

Trans. Amer. Math. Soc. 226 (1977), 181-189 Request permission

Analogues of classical representation formulas for entire functions of exponential type are proved in the class of discrete analytic functions.

References

Jacqueline Ferrand, Fonctions préharmoniques et fonctions préholomorphes, Bull. Sci. Math. (2) 68 (1944), 152–180 (French). MR 13411
R. J. Duffin, Basic properties of discrete analytic functions, Duke Math. J. 23 (1956), 335–363. MR 78441, DOI 10.1215/S0012-7094-56-02332-8
Ralph Philip Boas Jr., Entire functions, Academic Press, Inc., New York, 1954. MR 0068627
Leon Ehrenpreis, Fourier analysis in several complex variables, Pure and Applied Mathematics, Vol. XVII, Wiley-Interscience [A division of John Wiley & Sons, Inc.], New York-London-Sydney, 1970. MR 0285849
Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
Angus E. Taylor, Introduction to functional analysis, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0098966
Walter Rudin, Real and complex analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210528
V. P. Havin, Spaces of analytic functions, Math. Analysis 1964 (Russian), Akad. Nauk SSSR Inst. Naučn. Informacii, Moscow, 1966, pp. 76–164 (Russian). MR 0206694
Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696