Geodesic
The resolvent structure of a~Volterra equation with nonsummable difference kernel
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2010), pp. 72-82.

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In this paper we study the asymptotic behavior of the resolvent of a linear integral Volterra equation whose difference kernel is nonsummable. For a certain class of such kernels the equation is reducible to an equation whose difference kernel is summable. This enables one to use the well-known results on the structure of resolvents of summable kernels in the case of a nonsummable kernel. We apply the obtained results to homogeneous kernels of degree $-1$.
Keywords: linear integral Volterra equation, nonsummable kernel, resolvent structure, homogeneous kernel. 
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Z. B. Tsalyuk; M. V. Tsalyuk. The resolvent structure of a~Volterra equation with nonsummable difference kernel. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2010), pp. 72-82. http://geodesic.mathdoc.fr/item/IVM_2010_4_a7/

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