A reproducing kernel Hilbert space constructive approximation for integral equations with Toeplitz and Hankel kernels. (English) Zbl 1330.45005
Summary: 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.
MSC:
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 46E22 | Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) |
| 45L05 | Theoretical approximation of solutions to integral equations |
