We investigate weighted L p mean convergence of Grünwald interpolation operators based on the zeros of orthogonal polynomials with respect to a general weight and generalized Jacobi weights. We give necessary and sufficient conditions for such convergence for all continuous functions. 1. Introduction. In this paper, we study weighted L p (0 < p < ∞) mean con

‎Let $mathscr{L}$ be a commutative subspace lattice generated by finite many commuting independent nests on a complex separable Hilbert space $mathbf{H}$ with ${rm dim}hspace{2pt}mathbf{H}geq 3$‎, ‎${rm Alg}mathscr{L}$‎ ‎the CSL algebra associated with $mathscr{L}$ and $mathscr{M}$ be an algebra containing ${rm Alg}mathscr{L}$‎. ‎This article is aimed at describing the form of‎ ‎additive mapppi...

in this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted dirichlet spaces or bloch type spaces to $q_k$ type spaces.

A generalized version of the weighted-averages method is presented for the acceleration of convergence of sequences and series over a wide range of test problems, including linearly and logarithmically convergent series as well as monotone and alternating series. This method was originally developed in a partitionextrapolation procedure for accelerating the convergence of semiinfinite range int...

Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...

Attouch's Theorem, which gives on a reflexive Banach space the equivalence between the Mosco epi-convergence of a sequence of convex functions and the graph convergence of the associated sequence of subgradients, has many important applications in convex optimization. In particular, generalized derivatives have been defined in terms of the epi-convergence or graph convergence of certain differe...

The approximate solvability of a generalized system for nonlinear variational inequality in Hilbert spaces was studied, based on the convergence of projection methods. But little research was done in Banach space. The primary reason was that projection mapping lacked preferably property in Banach space. In this paper, we introduced the generalized projection methods. By using these methods, the...

We introduce a numerical method for extracting minimal geodesics along the group of volume preserving maps, equipped with the L metric, which as observed by Arnold [Arn66] solve the Euler equations of inviscid incompressible uids. The method relies on the generalized polar decomposition of Brenier [Bre91], numerically implemented through semi-discrete optimal transport. It is robust enough to e...