Abstract
An interpolant with orthonormal nodes is constructed for a polynomial operator of a given degree defined on an abstract Hilbert space. An estimate for the interpolation accuracy is derived in the metric of the space of operator values, while in the case where nodes are elements of a basis, the pointwise convergence of the interpolational operator process in this metric is proved as the number of nodes increases. Bibliography: 7 titles.
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Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 79, 1995, pp. 3–9
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Kashpur, E.F., Khlobystov, V.V. Interpolation of polynomial operators in a Hilbert space. J Math Sci 86, 2455–2458 (1997). https://doi.org/10.1007/BF02355308
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DOI: https://doi.org/10.1007/BF02355308