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	STUDIA MATHEMATICA - Ediţia nr.2 din 2010

	Articol:	THE SOLVABILITY AND PROPERTIES OF SOLUTIONS OF ONE WIENER-HOPF TYPE EQUATION IN THE SINGULAR CASE. Autori: .


	Rezumat: The work defines the conditions of solvability of one integral convolutional equation with degreely difference kernels in a singular case. This type of integral equations was not studied earlier, and it turned out that all methods used for the investigation of such equations with the help of Riemann boundary problem at the real axis are not applied there. The investigation of such type equations is based on the investigation of the equivalent singular integral equation with the Cauchy type kernel at the real axis in a singular case. It is determined that the equation is not a Noetherian one. Besides, there are shown the number of the linear independent solutions of the homogeneous equation and the number of conditions of solvability for the heterogeneous equation in the singular case. The general form of these conditions is also shown and there are determined the spaces of solutions of the equation. Thus the convolutional equation that wasn’t studied earlier is presented in this work and the theory of its solvability in the singular case is built here. So some new and interesting theoretical results are got in this paper. Key words and phrases. Integral convolutional equation, the number of the linear independent solutions, singular integral equation, Cauchy type kernel, a Noetherian type equation, conditions of solvability, index, spaces of solutions, singular case of solutions.




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