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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Binary operations in the set of solutions of a partial difference equation

Author: Doron Zeilberger
Journal: Proc. Amer. Math. Soc. 62 (1977), 242-244
MSC: Primary 39A05
MathSciNet review: 0440230
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Abstract: Let $ \mathcal{P}$ be a partial difference operator with constant coefficients in n independent (discrete) variables, and let $ {\mathcal{S}_\mathcal{P}} = \{ f:{Z^n} \to {\mathbf{C}};\mathcal{P}f = 0\} $. We introduce a certain class of binary operations $ {\mathcal{S}_\mathcal{P}} \times {\mathcal{S}_\mathcal{P}} \to {\mathcal{S}_\mathcal{P}}$ generalizing a binary operation introduced by Duffin and Rohrer.

References [Enhancements On Off] (What's this?)

  • [1] R. J. Duffin and Joan Rohrer Hundhausen, A convolution product for the solutions of partial difference equations, Duke Math. J. 35 (1968), 683-698. MR 39 # 1831. MR 0240484 (39:1831)
  • [2] R. J. Duffin and C. S. Duris, A convolution product for discrete function theory, Duke Math. J. 31 (1964), 199-220. MR 29 #429. MR 0163126 (29:429)

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PII: S 0002-9939(1977)0440230-3
Article copyright: © Copyright 1977 American Mathematical Society

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