Harmonic approximation and Sarason's-type theorem

Harmonic approximation and Sarason's-type theorem

In the present paper, we study uniform approximation of bounded functions on an open subset of the Euclidean space d by means of harmonic functions arising as solutions of the classical or generalized Dirichlet problem. As a consequence of results obtained we establish a harmonic analogue of Sarason’s H + C – theorem; see e. g. [5]. We shall consider an arbitrary bounded open subset of , d ≥ 2....

Wolstenholme Type Theorem for Multiple Harmonic Sums

for complex variables s1, . . . , sl satisfying Re(sj) + · · · + Re(sl) > l − j + 1 for all j = 1, . . . , l. We call |s| = s1 + · · · + sl the weight and denote the length by l(s). The special values of multiple zeta functions at positive integers have significant arithmetic and algebraic meanings, whose defining series (1.1) will be called MZV series, including the divergent ones like ζ(. . ....

fragmentability and approximation

in chapter 1, charactrizations of fragmentability, which are obtained by namioka (37), ribarska (45) and kenderov-moors (32), are given. also the connection between fragmentability and its variants and other topics in banach spaces such as analytic space, the radone-nikodym property, differentiability of convex functions, kadec renorming are discussed. in chapter 2, we use game characterization...

Matrix Summability and Korovkin Type Approximation Theorem on Modular Spaces

In this paper, using a matrix summability method we obtain a Korovkin type approximation theorem for a sequence of positive linear operators defined on a modular space.

A Fatou-type Theorem for Harmonic Functions on Symmetric Spaces