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Recursive subnormal completion and the truncated moment problem. (English) Zbl 1027.44003
Summary: The aim of this paper is to study properties of sequences that are recursively defined by a linear equation and their applications to the truncated moment problem in connection with the problem of subnormal completion of the truncated weighted shifts. Special cases are considered and some classical results due to J. G. Stampfli [Pac. J. Math. 17, 367-379 (1966; Zbl 0189.43902)], R. E. Curto and L. A Fialkow [Mem. Am. Math. Soc. 568 (1996; Zbl 0876.30033)] are recovered using elementary techniques.

44A20 Integral transforms of special functions
47A57 Linear operator methods in interpolation, moment and extension problems
47B20 Subnormal operators, hyponormal operators, etc.
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