On the Theory of Convolution Integral Equations Related to Lebedev’s Type Operators
DOI:
https://doi.org/10.5644/SJM.05.1.11Keywords:
Convolution integral equations, singular equations, Kontorovich-Lebedev transform, modified Bessel function, Fourier transform, Riemann boundary value problem, Cauchy's kernel, Banach ringAbstract
We draw a parallel with the Gakhov-Cherskii method to investigate a class of convolution integral equations related to the Kontorovich-Lebedev and Lebedev's type transformations. A relationship with the Cauchy type integral is obtained. The general convolution equation is solved being reduced to the Riemann boundary value problem by means of the Kontorovich-Lebedev transform.
2000 Mathematics Subject Classification. 45A05, 45E05, 44A15, 33C10, 30E20, 30E25
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