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Complete systems of Kummer and Weber-Hermite functions in spaces of holomorphic functions. (English) Zbl 0845.30002

Behara, Minaketan (ed.) et al., Proceedings of the 2nd Gauss symposium. Conference A: Mathematics and theoretical physics, Munich, Germany, August 2-7, 1993. Berlin: Walter de Gruyter. Symposia Gaussiana. 723-731 (1995).
Summary: Let \(\Phi(a, c; z)\) be the Kummer confluent hypergeometric function with parameters \(a\) and \(c\), \(D_\nu(z)\) be the Weber-Hermite function with index \(\nu\) and let \(\{k_n\}^\infty_{n= 0}\) be an increasing sequence of non-negative integers. In the paper sufficient conditions for the completeness of the systems \(\{\Phi(\pm(k_n+ \lambda), \alpha+ 1; z)\}^\infty_{n= 0}\) and \(\{D_{\pm(k_n+ \lambda)}(z)\}^\infty_{n= 0}\) in spaces of holomorphic functions are given in terms of the density of the sequence \(\{k_n\}^\infty_{n= 0}\).
For the entire collection see [Zbl 0828.00029].

MSC:

30B60 Completeness problems, closure of a system of functions of one complex variable
33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)
42C30 Completeness of sets of functions in nontrigonometric harmonic analysis
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