Estimation of the Lebesgue constant of interpolated rational processes with special nodes
https://doi.org/10.29235/1561-2430-2026-62-2-95-101
Abstract
Fourier series and interpolation processes possess an important property: their rate of convergence can be upper-bounded if the estimates of the best approximations and Lebesgue constants are known. Lebesgue constants in the polynomial case have been extensively studied. For rational Fourier series, they were estimated by G. S. Kocharyan (1958), and for rational interpolation processes, they have been studied since the works of V. N. Rusak (1962). However, in each case, the estimates were obtained under rather strict restrictions on the poles. In this work, the estimates of Lebesgue constants of interpolating rational trigonometric processes are obtained under conditions of completeness of the corresponding system of rational functions.
About the Authors
Ya. A. Rouba
Yanka Kupala State University of Grodno
Belarus
Belarus
Yauheni A. Rouba – Dr. Sc. (Physics and Mathematics), Professor, Professor of the Department of Fundamental and Applied Mathematics
22, Ozheshko Str., 230023, Grodno
A. V. Trusila
Yanka Kupala State University of Grodno
Belarus
Belarus
Anzhalika V. Trusila – Master Student of the Department of Mathematical Analysis, Differential Equations and Algebra
22, Ozheshko Str., 230023, Grodno
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