Kergin Approximation in Banach Spaces

Holomorphic Approximation in Banach Spaces: A survey

We give a survey about the Runge approximation problem for a holomorphic function defined on the unit ball of a complex Banach space.

Approximation theorems for Banach-valued almost periodic and semi-almost periodic holomorphic functions

The paper studies semi-almost periodic holomorphic functions on a polydisk which have, in a sense, the weakest possible discontinuities on the boundary torus. The basic result used in the proofs is an extension of the classical Bohr approximation theorem for almost periodic holomorphic functions on a strip to the case of Banach-valued almost periodic holomorphic functions.

Linear polynomial approximation schemes in Banach holomorphic function spaces

Let $X$ be a Banach holomorphic function space on the unit disk. A linear polynomial approximation scheme for $X$ is a sequence of bounded linear operators $T_n:X\to X$ with the property that, for each $f\in X$, the functions $T_n(f)$ are polynomials converging to $f$ in the norm of the space. We completely characterize those spaces $X$ that admit a linear polynomial approximation scheme. In particular, we show that it is NOT sufficient merely that polynomials be dense in $X$.

Extensions and approximations of Banach-valued Sobolev functions

In complete metric measure spaces equipped with a doubling measure and supporting a weak Poincaré inequality, we investigate when a given Banach-valued Sobolev function defined on a subset satisfying a measure-density condition is the restriction of a Banach-valued Sobolev function defined on the whole space. We investigate the problem for Hajłasz- and Newton-Sobolev spaces, respectively. First, we show that Hajłasz-Sobolev extendability is independent of the target Banach spaces. We also show that every $c_0$-valued Newton-Sobolev extension set is a Banach-valued Newton-Sobolev extension set …

多圆盘上Banach值${\mathbf H^\infty}$函数的Runge型逼近定理

Runge-Type Approximation Theorem for Banach-valued ${\mathbf H^\infty}$ Functions on a Polydisk

该研究证明多圆盘上Banach值有界全纯函数的Runge型逼近定理，推广Suárez的相关结果，可应用于高维日冕问题。