Open AccessFunction Polynomization Methods and their Applications
Author(s) -
А. Д. Нахман
Publication year - 2020
Publication title -
vestnik tambovskogo gosudarstvennogo tehničeskogo universiteta
Language(s) - English
Resource type - Journals
eISSN - 2542-1409
pISSN - 0136-5835
DOI - 10.17277/vestnik.2020.03.pp.437-449
Subject(s) - mathematics , quasiconvex function , lebesgue integration , sequence (biology) , fourier series , chebyshev filter , class (philosophy) , pure mathematics , mathematical analysis , metric space , space (punctuation) , function (biology) , power series , convergence (economics) , regular polygon , subderivative , geometry , computer science , convex optimization , artificial intelligence , evolutionary biology , biology , genetics , operating system , economics , economic growth
A class of semicontinuous quasiconvex methods of summation of Fourier – Chebyshev series is studied. Upper bounds are obtained for the norms of the corresponding operators in the space of continuous functions. The convergence of means in the metric of space is established. The summability at break points of the first kind is also considered. Processes for restoring functions from a given sequence of power moments are proposed. Ways of generalizing the results and extending them to the case of summability at Lebesgue points are indicated.