Fundamental Operator-Valued Functions of Singular Integrodifferential Operators in Banach Spaces
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In this paper, using methods of the theory of generalized functions in Banach spaces, we examine the Cauchy problem for an abstract integrodifferential equation of a specific type. Under the assumption that there exist the complete Jordan structure of the differential part of the equation and the order of the zero of the kernel of the integral part, the fundamental operator-valued function (the fundamental solution) is constructed for the corresponding integrodifferential operator, which is used for further investigation of the problem.
KeywordsBanach space Fredholm operator generalized function fundamental solution
AMS Subject Classification34G10 45K05 45N05
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