Geodesic
Degenerate integro-differential operators in Banach spaces and their applications
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2011), pp. 68-79

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In this paper we consider linear integro-differential equations in Banach spaces with Fredholm operators at the highest-order derivatives and convolution-type Volterra integral parts. We obtain sufficient conditions for the unique solvability (in the classical sense) of the Cauchy problem for the mentioned equations and illustrate the abstract results with pithy examples. The studies are carried out in classes of distributions in Banach spaces with the help of the theory of fundamental operator functions of degenerate integro-differential operators. We propose a universal technique for proving theorems on the form of fundamental operator functions.
Keywords: Banach spaces, Fredholm operator, Jordan sets, fundamental operator functions.
Mots-clés : distributions 
@article{IVM_2011_10_a7,
     author = {M. V. Falaleev and S. S. Orlov},
     title = {Degenerate integro-differential operators in {Banach} spaces and their applications},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {68--79},
     publisher = {mathdoc},
     number = {10},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_10_a7/}
}
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M. V. Falaleev; S. S. Orlov. Degenerate integro-differential operators in Banach spaces and their applications. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2011), pp. 68-79. http://geodesic.mathdoc.fr/item/IVM_2011_10_a7/