Approximation by Entire Functions of Exponential Type and Generalized Smoothness

Student: Krasilnikova Viktoriya

Supervisor: Sergey Artamonov

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Control Systems and Data Processing in Engineering (Master)

Year of Graduation: 2020

In this paper, we consider the moduli of smoothness ωβ(f, δ)p, 0 < β < 1, related to the Riesz derivative of order β. We prove the equivalence of the modulus of smoothness ω<β>(f, δ)p to the error in the approximation of convolution integrals generated by the Riesz kernel and the equivalence K-functional related to the Riesz derivative.

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