We consider reproducing kernel Hilbert spaces of Dirichlet series with kernels of the form k(s, u) = ∑ ann −s−ū, and characterize when such a space is a complete Pick space. We then discuss what it means for two reproducing kernel Hilbert spaces to be “the same”, and introduce a notion of weak isomorphism. Many of the spaces we consider turn out to be weakly isomorphic as reproducing kernel Hil...

In this paper, a numerical scheme for solving singular initial/boundary value problems presented.By applying the reproducing kernel Hilbert space method (RKHSM) for solving these problems,this method obtained to approximated solution. Numerical examples are given to demonstrate theaccuracy of the present method. The result obtained by the method and the exact solution are foundto be in good agr...

Abstract In this paper, we will present a new method for a Volterra integral equation with weakly singular kernel in the reproducing kernel space. Firstly the equation is transformed into a new equivalent equation. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximation un(t) to the exact solution u(t) is obtained. Some...

We consider the reproducing kernel Hilbert space Hμ induced by a kernel which is obtained using the Fourier-Stieltjes transform of a regular, positive, finite Borel measure μ on a locally compact abelian topological group Γ. Denote by G the dual of Γ. We determine Hμ as a certain subspace of the space C0(G) of all continuous function on G vanishing at infinity. Our main application is calculati...

in this paper at first , we discuss about nonlinear pseudoparabolic equations with nonlocalboundary conditions and their results.at second we use an effective error estimation for this method altough has not yet beendiscussed. the aim of this paper is to fill this gap.

where (Ω,μ) is a probability space. The kernel K is used to generate a Hilbert space, known as a reproducing kernel Hilbert space, whose unit ball is the class of functions we investigate. Recall that if K is a positive definite function K : Ω×Ω → R, then by Mercer’s Theorem there is an orthonormal basis (φi)i=1 of L2(μ) such that μ× μ almost surely, K(x,y) = ∑i=1 λiφi(x)φi(y), where (λi)i=1 is...