On interpolation of polynomial operators
type: Item
instance of: scholarly article
title: On interpolation of polynomial operators
zbMATH Open document ID: 0887.41005
DOI: 10.1007/BF02366503
author: V. V. Khlobystov
author: E. E. Kashpur
published in: Cybernetics and Systems Analysis
publication date: 1997-10-06T00:00:00Z
review text: In this paper the authors construct an operator interpolant for a polynomial operator on an orthonormal system of knots in a Hilbert space. For the construction of this interpolant, the authors generalize at the operator level the method of orthogonal moments, which is used in problems of identification of a polynomial functional system with subsequent application of the scheme for separation of homogeneous functions. The interpolant accuracy is then estimated for the constructed interpolant; for the case when the orthonormal system of knots is a basis of the space, the accuracy bound leads to pointwise convergence of the operator interpolation process as the number of knots increases. Such a convergence example is considered for a regular functional polynomial of second degree defined on periodic functions whose derivatives are of bounded variation. (from the authors' introduction to the paper).
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 1051097
zbMATH Keywords: interpolation, polynomial operator, convergence
reviewed by: Y. Sitaraman
MaRDI profile type: Publication
cites work: A Weierstrass theorem for real, separable Hilbert spaces
cites work: A Weierstrass theorem for real Banach spaces
cites work: On polynomial approximation of operators
cites work: Q3891666
cites work: Synthesis of Polynomic Systems
cites work: Lagrange and Hermite interpolation in Banach spaces
cites work: Q4278557
cites work: Q4315960
cites work: Polynomial interpolation of operators
cites work: Q4851231
cites work: Q3955205
cites work: Measurement of the Kernels of a Non-linear System of Finite Order†
description: scientific article; zbMATH DE number 1051097