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CNAA / Theses / 2009 / June /

Criterii noetheriene pentru unele ecuaţii integrale în convoluţii cu nuclee polinomiale


Author: Scerbacova Alexandra
Degree:doctor of physics and mathematics
Speciality: 01.01.01 - Mathematical analysis
Year:2009
Scientific adviser: Vasile Neagu
doctor habilitat, professor, Moldova State University
Institution:
Scientific council:

Status

The thesis was presented on the 19 June, 2009
Approved by NCAA on the 1 October, 2009

Abstract

Adobe PDF document – 0.36 Mb / in romanian

Keywords

Integral equations of the convolutional type with polynomial kernels, singular integral equations with Cauchy kernel, integral Fourier transformation, Rieman differential boundary problems, symbol of singular integral equation, conditions of solvability, Noether conditions, index, compactness of a regular operator, linear independent solutions, integral representation, particular indexes

Summary

The work is devoted to obtaining conditions of Noether for integral equations of the convolutional type with polynomial kernels in the normal and singular cases, to studying the conditions of their normal solvability and the properties of solutions constructed there. The equivalent singular integral equations with the Cauchy kernel at the real axis for these integral equations were constructed here. Studying of Noether conditions and conditions of the existence of solutions in the normal and singular cases was made here basing on Noether conditions and conditions of the existence of solutions for singular integral equations with Cauchy kernel. The conditions of solvability for a singular integral equation with Cauchy kernel in the singular case were also established here basing on the conditions of the solvability for the equivalent Rieman boundary problem in the singular case. A very important role there played integral representations for functions and derivatives of them, which are analytical in the upper and lower half planes of the complex plane that permitted to transform Rieman boundary problems into singular integral equations with Cauchy kernel. Spaces of solutions of integral equations of the convolutional type considered here in normal and singular cases were defined and studyed in that work. The analogous results for some systems of the integral equations of the convolutional type are also obtained here.

The Ph. D. thesis is written in Russian.