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Polynomial interpolation of operators

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Abstract

Necessary and sufficient conditions for the solvability of the polynomial operator interpolation problem in an arbitrary vector space are obtained (for the existence of a Hermite-type operator polynomial, conditions are obtained in a Hilbert space). Interpolational operator formulas describing the whole set of interpolants in these spaces as well as a subset of those polynomials preserving operator polynomials of the corresponding degree are constructed. In the metric of a measure space of operators, an accuracy estimate is obtained and a theorem on the convergence of interpolational operator processes is proved for polynomial operators. Applications of the operator interpolation to the solution of some problems are described. Bibliography: 134 titles.

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  1. V. L. Makarov
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  2. V. V. Khlobystov
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Additional information

This paper is a continuation of the work published inObchyslyuval'na ta Prykladna Maternatyka, No. 78 (1994). The numeration of chapters, assertions, and formulas is continued.

Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 79, 1995, pp 10–116.

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Makarov, V.L., Khlobystov, V.V. Polynomial interpolation of operators. J Math Sci 86, 2459–2521 (1997). https://doi.org/10.1007/BF02355309

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