On the solvability of a class of Volterra operator equations of the first kind with piecewise continuous kernels.

*(English. Russian original)*Zbl 1328.47015
Math. Notes 96, No. 6, 811-826 (2014); translation from Mat. Zametki 96, No. 5, 773-789 (2014).

Summary: We obtain sufficient conditions for the existence and uniqueness of continuous solutions of Volterra operator equations of the first kind with piecewise determined kernels. For the case in which the solution is not unique, we prove existence theorems for the parametric families of solutions and present their asymptotics in the form of logarithmic polynomials.

##### MSC:

47A50 | Equations and inequalities involving linear operators, with vector unknowns |

45D05 | Volterra integral equations |

##### Keywords:

Volterra operator equation; Banach space; asymptotic approximation; successive approximation method; Fredholm point; Fredholm operator; Jordan set
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\textit{N. A. Sidorov} and \textit{D. N. Sidorov}, Math. Notes 96, No. 6, 811--826 (2014; Zbl 1328.47015); translation from Mat. Zametki 96, No. 5, 773--789 (2014)

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##### References:

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