n-Best kernel approximation in reproducing kernel Hilbert spaces

By making a seminal use of the maximum modulus principle of holomorphic functions we prove existence of n-b est kernel approximation for a wide class of reproducing kernel Hilbert spaces of holomorphic functions in the unit disc, and for the corresponding class of Bochner type spaces of stochastic processes. This study thus generalizes the classical result of n-b est rational approximation for the Hardy space and a recent result of n-b est kernel approximation for the weighted Bergman spaces of the unit disc. The type of approximations has significant applications to signal and image processing and system identification, as well as to numerical solutions of the classical and the stochastic type integral and differential equations.& COPY; 2023 Published by Elsevier Inc.