Interpolation formulas for operators defined on functional Banach algebras
https://doi.org/10.29235/1561-2430-2024-60-4-295-302
Abstract
This article is devoted to the problem of interpolation of operators defined on Banach algebras of functions. Interpolation operator polynomials in the Lagrange and Newton forms of arbitrary fixed degree, containing the operation of multiplying elements of functional algebra, are obtained as solutions of the corresponding problems of single operator interpolation. The construction of interpolation formulas of the Newton’s structure is based on apparatus of operator separated differences. Classes of operator polynomials are indicated that are typical for functional Banach algebras under consideration, with respect to which the presented interpolation formulas are invariant. Explicit representations of the operator interpolation error are obtained. Special cases of linear interpolation formulas are considered, when the multiplication operation is given by various rules for convolution of elements of functional algebra. Corresponding first-order interpolation formulas are constructed, which contain the Fourier or Laplace transforms and are exact for linear operator polynomials of a special form.
Keywords
Banach algebra,
convolution operator,
operator interpolation of Lagrange type,
Dirac delta function,
Fourier transform,
Heaviside function,
Laplace transform
Supporting agencies: This work was supported by the State Program of Scientific Research “Convergence-2025”, subprogram “Mathematical models and methods”, task 1.4.01.2.
About the Author
M. V. Ignatenk
Belarusian State University
Belarus
Belarus
Marina V. Ignatenko – Ph. D. (Physics and Mathematics), Associate Professor, Head of Web-Technologies and Computer Simulation Department
4, Nezavisimosti Ave., 220030, Minsk
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