Let κ be an U-invariant reproducing kernel and let H (κ) denote the reproducing kernel Hilbert C[z1, . . . , zd]-module associated with the kernel κ. Let Mz denote the d-tuple of multiplication operators Mz1 , . . . ,Mzd on H (κ). For a positive integer ν and d-tuple T = (T1, . . . , Td), consider the defect operator

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 soluti...

In this paper, we present a new method for solving Reproducing Kernel Space (RKS) theory, and iterative algorithm for solving Generalized Burgers Equation (GBE) is presented. The analytical solution is shown in a series in a RKS, and the approximate solution u(x,t) is constructed by truncating the series. The convergence of u(x,t) to the analytical solution is also proved.

Abstract This short note has to make alive the overlooked work of Pedrick. It is rather a tour guide than exhausted examination content and intends serve potential explorers diverse kinds reproducing kernel (Hilbert) spaces, topic mushrooming nowadays.