1. Let A be a fixed compact Hausdorff space, C the Banach lattice of continuous real functions on X, L its dual, and M its second dual. The closure of C in M under the weak topology wiM, L) determined by L is, as is well known, M itself. In fact, the closure of C under the Mackey topology riM, L) is M itself, by the Grothendieck Theorem. A deeper property is that this relationship between C and...

Nyström method has been successfully used to improve the computational efficiency of kernel ridge regression (KRR). Recently, theoretical analysis of Nyström KRR, including generalization bound and convergence rate, has been established based on reproducing kernel Hilbert space (RKHS) associated with the symmetric positive semi-definite kernel. However, in real world applications, RKHS is not a...

Abstract The generalized Schwarz algorithm for a class of elliptic quasi-variational inequalities related to impulse control problems is studied in this paper. principal result prove the error estimate $L^{\infty}$ L ∞ -norm m subdomains with overlapping nonmatching gri...

In this paper, we generalize the concept of unbounded norm (un) convergence: let X be a normed lattice and Y a vector lattice such that X is an order dense ideal in Y ; we say that a net (yα) un-converges to y in Y with respect to X if ∥∥|yα−y|∧x∥∥→ 0 for every x ∈ X+. We extend several known results about unconvergence and un-topology to this new setting. We consider the special case when Y is...

A physical-mathematical approach to anomalous diffusion is based on a generalized diffusion equation containing derivatives of fractional order. In this paper, an anomalous sub-diffusion equation (ASub-DE) is considered. A new implicit numerical method (INM) and two solution techniques for improving the order of convergence of the INM for solving the ASub-DE are proposed. The stability and conv...

We perform a convergence analysis for discretization of Helmholtz scattering and resonance problems obtained by Hardy space infinite elements. Super-algebraic convergence with respect to the number of Hardy space degrees of freedom is achieved. As transparent boundary spheres and piecewise polytopes are considered. The analysis is based on a G̊arding-type inequality and standard operator theoret...

In this paper we provide a detailed convergence analysis for an unconditionally energy stable, second order accurate convex splitting scheme for the modified phase field crystal equation, a generalized damped wave equation for which the usual phase field crystal equation is a special degenerate case. The fully discrete, fully second order finite difference scheme in question was derived in a re...