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A reproducing kernel Hilbert space constructive approximation for integral equations with Toeplitz and Hankel kernels
A reproducing kernel Hilbert space approach is proposed to study a class of integral equations with Toeplitz and Hankel kernel functions. The existence property and approximate representations of the solutions are given by constructing appropriate auxiliary operators and positive definite matrices within a reproducing kernel Hilbert space framework. Moreover, conditions for the boundedness and uniqueness of the solution are also obtained.
Integral equation, best approximation, positive definite matrix, Moore-Penrose generalized inverse, Hilbert space, reproducing kernel, convolution, Toeplitz kernel, Hankel kernel, Aveiro discretization method.