Cherems'ka N. The Sequences of Infinite Rank Nonstationarity in Hilbert Space

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0401U000256

Thesis Registration Form

0401U000256.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

28-12-2000

Specialized Academic Board

К 64.051.11

V.N. Karazin Kharkiv National University

Essay

3. A new approach to study the sequences of infinite rank of nonsta tionarity in Hildert space is developed. New characteristics for the nonstationarity such as correlation difference,quasi-rank,etc.,have been introduced to discribe the nonstationarity of sequence and to bind its correlation with dimension of non-Hermitian subspace for the operators which specify a respec tive sequence in Hilbert space. The spectral theory of nonselfconjugateoperators is applied to study the structure of correlation differences for some classes of nonstatio nary sequences and inhomogeneous fields in Hilbert space. A new approach allowing to obtain spectral representation of the nonstatio nary sequences is implemented based on analysis of invariant sub spaces for operators giving evolutional representation forsequences.

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