Abstract
Let H(ℂN) denote the Fréchet space of all entire functions of N variables (N≥1). The purpose of this paper is to prove the existence of a dense set of functions f in H(ℂN) such that if L is any nonscalar linear differential operator with constant coefficients, then the set {p(L)f∶p(·) is a polynomial} is dense in H(ℂN).
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References
K. C. Chan, Common cyclic vectors for operator algebras on spaces of analytic functions, Indiana Univ. Math. J., to appear.
R. M. Gethner; J. H. Shapiro, Universal vectors for operators on spaces of holomorphic functions, Proc. Amer. Math. Soc. vol. 100, no. 2, 1987, 281–288.
G. Godefroy; J. H. Shapiro, Operators with dense invariant cyclic vector manifolds. Preprint.
G. R. MacLane, Sequences of derivatives and normal families, J. Analyse Math. 2 (1952), 72–87.
W. Wogen, On some operators with cyclic vectors, Indiana Univ. Math. J. 27 (1978), 163–171.
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Research supported in part by an NSF grant
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Chan, K.C. Common cyclic entire functions for partial differential operators. Integr equ oper theory 13, 132–137 (1990). https://doi.org/10.1007/BF01195296
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DOI: https://doi.org/10.1007/BF01195296