The finite Hartley new convolutions and solvability of the integral equations with Toeplitz plus Hankel kernels (Q1759918)

In this article, integral equations of convolution type with a sum of a Toeplitz and a Hankel kernel are considered. The authors construct eight new generalized convolutions for the finite Hartley transforms. Additionally, they obtain both a necessary and sufficient condition for the unique solvability in \(L^2\). Note that this solvability condition is different from Tsitsiklis and Levy due to the convolution approach [\textit{J. N. Tsitsiklis} and \textit{B. C. Levy}, ``Integral equations and resolvents of Toeplitz plus Hankel kernels'', Technical Report LIDS-P-1170, Laboratory for Information and Decision Systems, M.I.T., December 1981, \url{http://www.mit.edu/~jnt/Papers/R-81-levy-hankel.pdf}].