Complex interpolation and complementably minimal spaces

The Banach space S is complementably minimal and subsequentially prime

We first include a result of the second author showing that the Banach space S is complementably minimal. We then show that every block sequence of the unit vector basis of S has a subsequence which spans a space isomorphic to its square. By the Pełczyński decomposition method it follows that every basic sequence in S which spans a space complemented in S has a subsequence which spans a space isomorphic to S (i.e. S is a subsequentially prime space).

Minimal Norm Interpolation in Harmonic Hilbert Spaces and Wiener Amalgam Spaces on Locally Compact Abelian Groups

The family of harmonic Hilbert spaces is a natural enlargement of those classical $L^{2}$-Sobolev space on $\R^d$ which consist of continuous functions. In the present paper we demonstrate that the use of basic results from the theory of Wiener amalgam spaces allows to establish fundamental properties of harmonic Hilbert spaces even if they are defined over an arbitrary locally compact abelian group $\G$. Even for $\G = \R^{d}$ this new approach improves previously known results. In this paper we present results on minimal norm interpolators over lattices and show that the infinite minimal nor…

Local interpolation for minimal surfaces

Let $a: I\to \mathbb{R}^3 $ be a real analytic curve satisfying some conditions. In this article, we show that for any real analytic curve $l:I\to \mathbb R^3$ close to $a$ (in a sense which is precisely defined in the paper) there exists a translation of $l$, and a minimal surface which contains both $ a $ and the translated $l$.

极大曲面与极小曲面的插值

Interpolation by maximal and minimal surfaces

本文利用巴拿赫空间反函数定理，通过构造极大曲面和极小曲面，分别对洛伦兹-闵可夫斯基空间和欧几里得空间中的实解析曲线进行插值，其中比约林问题和施瓦茨解起关键作用。

Hardy 和 Bergman 空间中的最优插值：再生核 Banach 空间方法

Optimal interpolation in Hardy and Bergman spaces: a reproducing kernel Banach space approach

本文利用再生核 Banach 空间框架和半内积，为 Hardy 和 Bergman 空间等函数空间中的插值问题提供了寻找最小范数解的系统方法，并给出数值示例。

Tangential interpolation in weighted vector-valued H^p spaces, with applications

In this paper, norm estimates are obtained for the problem of minimal-norm tangential interpolation by vector-valued analytic functions in weighted H^p spaces, expressed in terms of the Carleson constants of related scalar measures. Applications are given to the notion of p-controllability properties of linear semigroup systems and controllability by functions in certain Sobolev spaces.