Silenko V. Problems of Pompeiu type on the hyperbolic plane

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0410U001640

Thesis Registration Form

0410U001640.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

10-03-2010

Specialized Academic Board

K 11.193.02

Essay

It is for the first time, for the group of the translations of the hyperbolic plane, that the precise conditions of growth of under which some hyperbolic rectangle, or some hyperbolic four-sided set have the Pompeiu property have been determined in the thesis. The generalizations for two hyperbolic rectangles, two hyperbolic four-sided sets, several functions have been established. New theorems about inversion of the Pompeiu transform have also been obtained. The obtained results have been applied for determination of the new generalizations of the Morera function holomorphy theorem.

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