We investigate the construction of all reproducing kernel Hilbert spaces of functions on a domain Ω ⊂ R that have a countable sampling set Λ ⊂ Ω. We also characterize all the reproducing kernel Hilbert spaces that have a prescribed sampling set. Similar problems are considered for reproducing kernel Banach spaces, but now with respect to Λ as a p-sampling set. Unlike the general p-frames, we pr...

Support vector regression (SVR) has been regarded as a state-of-the-art method for approximation and regression. The importance of kernel function, which is so-called admissible support vector kernel (SV kernel) in SVR, has motivated many studies on its composition. The Gaussian kernel (RBF) is regarded as a “best” choice of SV kernel used by non-expert in SVR, whereas there is no evidence, exc...

Reproducing Kernel Hilbert Space (RKHS) and Reproducing Transformation Methods for Series Summation that allow analytically obtaining alternative representations for series in the finite form are developed.

The aim of this paper is to use the Reproducing kernel Hilbert Space Method (RKHSM) to solve the linear and nonlinear fuzzy impulsive fractional differential equations. Finding the numerical solutionsof this class of equations are a difficult topic to analyze. In this study, convergence analysis, estimations error and bounds errors are discussed in detail under some hypotheses which provi...

In this paper we propose a new approach for the modelling of the multi-variable systems (MIMO) on the Reproducing Kernel Hilbert Space (RKHS). The proposed approach considers the MIMO system as a set of MISO processes modelled in RKHS space. We propose also a comparative study of three identification kernel methods of nonlinear systems modelled in Reproducing Kernel Hilbert Space (RKHS), where ...

We prove that de Branges spaces of entire functions describe universality limits in the bulk for random matrices, in the unitary case. In particular, under mild conditions on a measure with compact support, we show that each possible universality limit is the reproducing kernel of a de Branges space of entire functions that equals a classical Paley-Wiener space. We also show that any such repro...