Karabash I. On similarity of differential operators to selfadjoint ones

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0405U003334

Thesis Registration Form

0405U003334.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

29-06-2005

Specialized Academic Board

К 11.193.02

Essay

Ordinary differential operators with an indefinite weight are considered. A question of similarity to selfadjoint or normal operators is studied. A criterion of similarity is obtained for the operator (sgn x) p(–i d/dx), where p(t) is a real polynomial. A criterion of similarity for the operator w(x) –1 p( i d/dx), where p(t) is real polynomial of odd order and w(x) is a step-function, is given. Similarity conditions in terms of Cauchy integrals and in terms of Weyl functions are given for the operator A = (sgn x)( -d2/dx2+q). For the case of a finite-zone potential the criterion of similarity is obtained.

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Files

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disser.pdf

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