Kyrylov S. Convergence of series over some orthonormal systems and estimates of coefficients

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0499U002613

Thesis Registration Form

0499U002613.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

08-10-1999

Specialized Academic Board

К 41.051.05

Essay

In the thesis the problem of convergence and unconditional convergence almost everywhere is investigated in case of series over orthnormal systems from the class introduced by the author. Norm estimates of functions over their Fourier coefficients are received in some functional spaces as well as conjugate estimates of coefficients. It is proved that the hypothesis which was proposed by Bullen and had deal with improvement of a Marcinkiewicz and Zygmund theorem is not true for general orthonormal systems.

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