The best joint approximation of some classes of functions in the Bergman space 𝐵_2
https://doi.org/10.22405/2226-8383-2024-25-5-183-194
Abstract
In this paper, we study several extreme problems related to the best joint approximation of certain classes of analytical functions in the unit circle given by higher-order continuity modules in the Bergman space 𝐵_2. It should be noted that for the first time the problem of joint approximation of periodic differentiable functions and their consecutive derivatives by trigonometric polynomials and their corresponding derivatives in a uniform metric was
investigated by A.L.Garkavi [1]. The results obtained in [1] were generalized by A.F.Timan [2] for a class of integer functions of exponential type on the entire line. In the monograph [3].
The problems of joint approximation are generalized to some classical theorems of the theory of approximation of functions. However, in the listed works, only asymptotically accurate results were obtained. In this paper, we prove a number of exact theorems for the joint approximation of analytic functions in the unit circle belonging to the Bergman space 𝐵_2, complementing the results of M.Sh.Shabozov [4].
About the Author
Khuromon Mamadamonovich Khuromonov
International University of Tourism and Entrepreneurship of Tajikistan
Tajikistan
Tajikistan
candidate of physical and mathematical sciences
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Review
For citations:
Khuromonov Kh.M. The best joint approximation of some classes of functions in the Bergman space 𝐵_2. Chebyshevskii Sbornik. 2024;25(5):183-194. (In Russ.) https://doi.org/10.22405/2226-8383-2024-25-5-183-194
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