REPRESENTATION OF SOLUTION FOR THE NONLINEAR OPERATOR EQUATIONS IN THE REPRODUCING KERNEL HILBERT SPACES

A reproducing kernel Hilbert space restricts the space of functions to smooth functions and has the ideal structure for function approximation and some aspects in learning theory. We discuss the structure of the solution space of some nonlinear operator equations in reproducing kernel Hilbert space. Actually, if the solution exists, we give the analytic representation of the minimal normal solution of the problem. We also try to review some of the basic facts regarding the reproducing kernel Hilbert spaces and their applications in approximation theory, learning theory as well as representation of the exact solution of some classes of nonlinear integral equations.

کلیدواژه ها:

Hilbert space ، reproducing kernel space ، kernel trick ، feature space ، nonlinear operator equations ، integral equations ، representer theorem