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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IVM_2010_4_a7,
     author = {Z. B. Tsalyuk and M. V. Tsalyuk},
     title = {The resolvent structure of {a~Volterra} equation with nonsummable difference kernel},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {72--82},
     publisher = {mathdoc},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_4_a7/}
}
TY  - JOUR
AU  - Z. B. Tsalyuk
AU  - M. V. Tsalyuk
TI  - The resolvent structure of a~Volterra equation with nonsummable difference kernel
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2010
SP  - 72
EP  - 82
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2010_4_a7/
LA  - ru
ID  - IVM_2010_4_a7
ER  - 
%0 Journal Article
%A Z. B. Tsalyuk
%A M. V. Tsalyuk
%T The resolvent structure of a~Volterra equation with nonsummable difference kernel
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2010
%P 72-82
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2010_4_a7/
%G ru
%F IVM_2010_4_a7
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/