in this letter, the numerical scheme of nonlinear volterra-fredholm integro-differential equations is proposed in a reproducing kernel hilbert space (rkhs). the method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satis ed. the nonlinear terms are replaced by its taylor series. in this technique, the nonlinear volterra-fredholm integr...

Another example of such a duality are the formulas of Gelfand-Tsetlin for matrix elements of irreducible representations of the algebra of complex matrices with trace 0 and the formulas for coordinates in the group of unitary matrices... In all of these cases the duality consists in the fact that functions of discrete arguments satisfy finite difference equations analogous to differential equat...

We consider various Hilbert spaces of Dirichlet series whose norms are given by weighted l2 norms of the Dirichlet coefficients. We characterize the multiplier algebras for some of these spaces. 0 Introduction Let w = {wn}n=n0 be a sequence of positive numbers. In this paper we are concerned with Hilbert spaces of functions representable by Dirichlet series: H w = {

Given a classical symmetric pair, (G, K), with g = Lie(G), we provide descriptions of the Hilbert series of the algebra of K-invariant vectors in the associated graded algebra of U(g) viewed as a K-representation under restriction of the adjoint representation. The description illuminates a certain stable behavior of the Hilbert series, which is investigated in a case-by-case basis. We note tha...