arXiv subjects

A. P. Starovoitov

Publications and source records attributed to A. P. Starovoitov.

2 recordsLinked to original sources

arXiv2025

Existence and explicit form of nonlinear Hermite-Chebyshev approximations

In this paper, sufficient conditions for the existence of trigonometric Hermite-Jacobi appro\-ximations of a system of functions that are sums of convergent Fourier series are found. Based on these results, sufficient conditions are established under which nonlinear Hermite-Chebyshev approximations of systems of functions representable by Fourier series in Chebyshev polynomials of the first and second kind exist. When the found conditions are met, explicit formulas are obtained for the numerators and denominators of trigonometric Hermite-Jacobi approximations and nonlinear Hermite-Chebyshev approximations of the first and second kind of the specified systems of functions.

math.CA↗

arXiv2025

Consistent rational approximations of power series, trigonometric series and series of Chebyshev polynomials

For trigonometric series and series of Chebyshev polynomials, we defined trigonometric Hermite-Padé and Hermite-Jacobi approximations, linear and nonlinear Hermite-Chebyshev approximations. We established criterion of the existence and uniqueness of trigonometric Hermite-Padé polynomials, associated with an arbitrary set of $k$ trigonometric series, and we found 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 are existed but aren't the same as trigonometric Hermite-Padé approximations. Similar examples were made for linear and nonlinear Hermite-Chebyshev approximations.

math.CA↗