Zagorodnyuk S. Spectral resolution of curves in Hilbert spaces

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0400U000314

Thesis Registration Form

0400U000314.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

24-12-1999

Specialized Academic Board

К64.051.11

Essay

New classes of nonstationary sequences in abstract Hilbert space are introduced and studied. Characterization of class of these sequences in terms of difference equations on correlation function is obtained. Number of ergodic theorems for sequences, corresponding classical systems of polynomials are proved. Systems of polynomials, corresponding to 5(diagonal, symmetric, semi(infinite matrix are considered. Examples are given, for which orthogonality relations are obtained. Some generalization of Hamburger moments problem is introduced and criteria of solvability of this problem is proved.

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