Differential-difference Equations in Entire Functions
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For a linear differential-difference equation with real shifts in the complex plane we prove a theorem of existence of entire solutions for an arbitrary entire function in the r.h.s. and, using it, show that the space of entire solutions of the corresponding homogeneous equation is infinite dimensional.
Mathematics Subject Classification (2000)Primary:30D05 Secondary:34K06
KeywordsLinear functional equations entire functions
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- Nörlund, N.E. Differenzenrechnung, Springer Verlag, Berlin, 1924.Google Scholar
- Gel’fond, A.O. Calculus of Finite Differences, Third corrected edition, Nauka, Moscow, 1967; English translation in: International Monographs on Advanced Mathematics and Physics, Hindustan Publishing Corp., Delhi, 1971.Google Scholar
- Naftalevich, A. Application of an iteration method for the solution of a difference equation, Matematicheskii Sbornik, 57 (99), 151–178, 1962.Google Scholar
- Levin, B.Ya. Lectures on Entire Functions, AMS, Translations of Mathematical Monographs, 150, 1996.Google Scholar
- Markuschevich, A.I. Theory of Analytic Functions, v. 2, Nauka, Moscow, 1968.Google Scholar