Geodesic
A note on spectral theory of integral-functional Volterra operators
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 17 (2024) no. 4, pp. 94-99

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A concise overview of the spectral theory of integral-functional operators is provided. In the context of analysis, a technique is described for deriving solutions to equations involving operators in a closed form. A constructive theorem has been established, outlining a procedure for determining the eigenvalues and eigenfunctions of these operators. Based on this theory, an analytical approach for generating solutions to a Volterra-type integro-functional inhomogeneous equation is proposed. The example illustrates the proposed theory.
Keywords: Volterra operator, eigenvalue, asymptotic approximation, integral-functional operator. 
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D. N. Sidorov. A note on spectral theory of integral-functional Volterra operators. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 17 (2024) no. 4, pp. 94-99. http://geodesic.mathdoc.fr/item/VYURU_2024_17_4_a7/