Оценки норм линейных операторов на множестве тригонометрических полиномов в пространстве L0
: магистерская диссертация

Translated title of the thesis: Estimates for norms of linear operators on the set of trigonometric polynomials in the space L0: Master's thesis

Student thesis: Master's Thesis

Abstract

We study a Bernstein inequality for a fractional derivative of order α ≥ 0 of a trigonometric polynomial in the space L0. In the case of zero order derivative, we obtain two-sided estimates for a sharp constant in this inequality, which show its behavior with respect to n. For positive and sufficiently small α, we obtain an upper estimate for a constant in the Bernstein inequality in L0. In the second part of the dissertation, we obtain estimates for norms in the space L0 of operators that set several higher or lower coefficients of a trigonometric polynomial to be zero.
Date of Award2015
Original languageRussian
Awarding Institution
  • Ural Federal University
SupervisorВиталий Владимирович Арестов (Supervisor)

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