Volchkov V. Convolution equations on symmetric spaces and their applications

Українська версія

Thesis for the degree of Doctor of Science (DSc)

State registration number

0510U000203

Thesis Registration Form

0510U000203.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

02-03-2010

Specialized Academic Board

Д 26.206.01

The Institute of Mathematics of NASU

Essay

The dissertation is devoted to the study of convolution equations on bounded domains of various homogeneous spaces. The theory of transmutation operators associated to eigenfunctions expansions of the Laplacian is developed. Effective description of solutions for a broad class of convolution equations is obtained. John type uniqueness theorems are proved. In many cases, the problem of nonzero solution existence for systems of convolution equations is solved. Delsart-Zalcman type two-radii problems are solved. Applications to complex analysis, the approximation theory and differential equations are found.

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