Наилучшее одностороннее интегральное приближение характеристической функции промежутка алгебраическими многочленами

: магистерская диссертация

Abstract

We consider the problems of the best one-sided approximation (from below and from above) in the space of functions integrable on (-1,1) with a weight to the characteristic function of an interval (a,b) from (-1,1) by the set of algebraic polynomials of degree not exceeding a given number. We solve the problems in the case when a and b are nodes of a positive quadrature formula under some conditions on its degree of precision as well as in the case of a symmetric interval for an even weight.

Date of Award	2019
Original language	Russian
Awarding Institution	Ural Federal University
Supervisor	Марина Валерьевна Дейкалова (Supervisor)