This article is cited in 1 paper

Real, Complex and Functional analysis

Rational approximations of power series, trigonometric series and series of Chebyshev polynomials

A. P. Starovoitov, I. V. Kruglikov, T. M. Osnach

Francisk Skorina Gomel State University, 104 Savieckaja Street, Gomiel 246028, Belarus

Abstract: In this paper, we defined trigonometric Hermite – Pade and Hermite – Jacobi approximations as well as linear and nonlinear Hermite – Chebyshev approximations for trigonometric and Chebyshev series. We established the criterion of the existence and uniqueness of trigonometric Hermite – Pade polynomials, associated with an arbitrary set of $k$ trigonometric series, and we found the explicit form of these polynomials. Similar results were obtained for linear Hermite – Chebyshev approximations. We made examples of systems of functions for which trigonometrical Hermite – Jacobi approximations existed which were not the same as trigonometric Hermite – Pade approximations. Similar examples were represented for linear and nonlinear Hermite – Chebyshev approximations.

Keywords: Hermite – Pade approximations; Pade – Chebyshev approximations; trigonometric series; series of Chebyshev polynomials

UDC: 517.538.52 + 517.538.53 + 517.518.84

Received: 30.08.2024
Revised: 04.10.2024
Accepted: 18.10.2024