2025/07/21 by Starovoitov, A. P., Kruglikov, I. V., Osnach, T. M.
#32E30 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #G.1.2
paper · doi:10.48550/arxiv.2507.15672
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.