Geodesic
Fundamental operator-valued functions of singular integrodifferential operators in Banach spaces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Tome 132 (2017), pp. 127-130

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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 investigations of the problem.
Keywords: Banach space, Fredholm operator, generalized function, fundamental solution. 
@article{INTO_2017_132_a28,
     author = {M. V. Falaleev},
     title = {Fundamental operator-valued functions of singular integrodifferential operators in {Banach} spaces},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {127--130},
     publisher = {mathdoc},
     volume = {132},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_132_a28/}
}
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M. V. Falaleev. Fundamental operator-valued functions of singular integrodifferential operators in Banach spaces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Tome 132 (2017), pp. 127-130. http://geodesic.mathdoc.fr/item/INTO_2017_132_a28/