Regularization in a functional reproducing kernel Hilbert space

We consider solving a system of semi-discrete first kind integral equations with right-hand-side being finite dimensional vector sampling values and propose regularization method for the in functional reproducing kernel Hilbert space (FRKHS), where linear functionals that define operator are continuous. A representer theorem is established, which reduces infinite problem to expresses its solution as combination FRKHS sessions. construct specific FRKHSs their associated kernels reconstruction function from Radon data, develop related methods reconstruction. present numerical results demonstrate proposed outperforms either traditional Tikhonov L2 or classical space.