On asymptotics of the spectrum of an integral operator with a logarithmic kernel of a special form. (English. Russian original) Zbl 1535.45009
Differ. Equ. 59, No. 12, 1721-1733 (2023); translation from Differ. Uravn. 59, No. 12, 1680-1691 (2023).
The author analyses a convolution-type equation on a finite interval having a kernel characterised by a logarithmic function whose argument depends on a hyperbolic cosine. The asymptotic behaviour of the spectrum of the integral operator associated with this equation is deduced by considering a corresponding conjugation problem for analytic functions and a resulting infinite system of linear algebraic equations.
Reviewer: Luis Filipe Pinheiro de Castro (Aveiro)
MSC:
| 45P05 | Integral operators |
| 45C05 | Eigenvalue problems for integral equations |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 45M05 | Asymptotics of solutions to integral equations |
| 47G10 | Integral operators |
References:
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| [7] | Polosin, A. A., On the asymptotic behavior of eigenvalues and eigenfunctions of an integral convolution operator with a logarithmic kernel on a finite interval, Differ. Equations, 58, 9, 1242-1257, (2022) · Zbl 1501.45001 · doi:10.1134/S0012266122090099 |
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