New Reproducing Kernel Functions

Distance Functions for Reproducing Kernel Hilbert Spaces

Suppose H is a space of functions on X. If H is a Hilbert space with reproducing kernel then that structure of H can be used to build distance functions on X. We describe some of those and their interpretations and interrelations. We also present some computational properties and examples.

Reproducing Kernel Functions Represented by Form of Polynomials

By re-defining the inner product of a reproducing kernel space, the reproducing kernel functions of that space can be represented by form of polynomials without changing any other conditions, and the higher order of the derivatives, the simpler of the reproducing kernel function expressions. Such expressions of reproducing kernel functions are the simplest from the computational point of view, ...

A New Approach for Solving Volterra Integral Equations Using The Reproducing Kernel ‎Method

This paper is concerned with a technique for solving Volterra integral equations in the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernel method, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series.An iterative method is given to obtain the approximate solution.The conver...

A new reproducing kernel method for solving Volterra integro-dierential equations

This paper is concerned with a technique for solving Volterra integro-dierential equationsin the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernelmethod, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series. An iterative method is given toobtain the...

Method of Reproducing Kernel