Geodesic
On the equiconvergence of expansions in eigen- and associated functions of an integral operator with involution
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2008), pp. 67-76

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In this paper we study an integral operator with involution. We solve the problem on the exact inversion of this operator, we obtain and study the integrodifferential system for the Fredholm resolvent and, finally, we prove the theorem on the equiconvergence of expansions in eigenfunctions and associated functions, in the ordinary trigonometric system.
Keywords: integral operator, resolvent, involution, eigenfunctions and associated functions, Fourier series. 
@article{IVM_2008_5_a7,
     author = {A. P. Khromov and L. P. Kuvardina},
     title = {On the equiconvergence of expansions in eigen- and associated functions of an integral operator with involution},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {67--76},
     publisher = {mathdoc},
     number = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_5_a7/}
}
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A. P. Khromov; L. P. Kuvardina. On the equiconvergence of expansions in eigen- and associated functions of an integral operator with involution. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2008), pp. 67-76. http://geodesic.mathdoc.fr/item/IVM_2008_5_a7/