Abstract
In the present paper, we consider the asymptotic behavior of the spectrum of a compact operator with difference kernel whose Fourier transform is equal to unity on some interval and is zero outside that interval.
This is a preview of subscription content, log in via an institution to check access.
References
Ukai, S., Asymptotic Distribution of Eigenvalues of the Kernel in the Kirkwood-Riseman Integral Equation, J. Math. Phys., 1971, vol. 12, no. 1, pp. 83–92.
Pal’tsev, B.V., Asymptotics of the Spectrum of Integral Convolution Operators on a Finite Interval with Homogeneous Polar Kernels, Izv. Ross. Akad. Nauk Ser. Mat., 2003, vol. 67, no. 4, pp. 67–154.
Gakhov, F.D. and Cherskii, Yu.I., Uravneniya tipa svertki (Equations of Convolution Type), Moscow: Nauka, 1978.
Author information
Authors and Affiliations
Additional information
Original Russian Text © A.A. Polosin, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 10, pp. 1516–1520.
Rights and permissions
About this article
Cite this article
Polosin, A.A. Asymptotic behavior of the spectrum of a convolution operator on a finite interval with the transform of the integral kernel being a characteristic function. Diff Equat 46, 1519–1523 (2010). https://doi.org/10.1134/S0012266110100186
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0012266110100186