An approach to RKHS inner products evaluation. Application to signal detection problem

The aim of this paper is to propose a new methodology based on Hilbert spaces with reproducing kernels (RKHS) obtained from the Rayleigh-Ritz method that allows us to evaluate a RKHS inner product approximately with the desired accuracy and obtain approximate series representations for second-order stochastic processes. Furthermore, we apply the introduced technique in the signal detection problem providing computationally feasible suboptimum detectors.