HILBERT SPACES OF FUNCTIONALS ASSOCIATED WITH NONLINEAR OPERATORS

Abstract

In [7] the subject of reproducing kernel Hilbert spaces (RKHSs) of linear functionals associated with linear operators and, in particular, with second-order generalized stochastic processes (GSPs), is pursued. In this work these ideas are extended to nonlinear operators. As an example the characteristic operator of a GSP is pursued. The so-called nonlinear space of the process associated with the characteristic operator is investigated and the RKHS of functionals isometrically isomorphic to it is constructed. Unlike the linear space, the nonlinear analysis is not limited to second order GSPs.