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Обобщенные сдвиги Бесселя и некоторые задачи теории приближений функций в метрике $L_{2}$. I

S. S. Platonov

Petrozavodsk State University, Faculty of Mathematics

Abstract: Some problems of aproximations of functions on half-interval $[0,+\infty )$ in the $L_{2}$-metric with certain weight by entire functions of exponential growth are studied. Modules of continuity which used in problems are constructed with help of generalized translations of Bessel. Direct theorems of Jacson type are proved. Nikolskii — Besov type function spaces are defined and their description are obtained in terms of the best approximations.

UDC: 517.5

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