Makarichev V. Application of atomic functions to the theory of generalized Taylor series, approximation theory and wavelet theory

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0414U005591

Thesis Registration Form

0414U005591.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

05-12-2020

Specialized Academic Board

К 64.051.11

V.N. Karazin Kharkiv National University

Essay

An existence of the asymptotics of the basic functions of a generalized Taylor series is proved. It is proved that spaces of linear combinations of the atomic functions shifts are asymptotically extremal for approximation of classes of periodic differentiable functions in the norm of L2. A new class of atomic functions is constructed and an existence of nonstationary infinitely differentiable wavelets with a compact support, which are finite linear combinations of these functions, is proved.

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Files

aref.rtf

dis.pdf

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