推导算子的通用公式及其应用

IF 0.6 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2024-06-03 DOI:10.1007/s10476-024-00028-7

J. Suárez de la Fuente

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引用次数: 0

摘要

我们给出了一个通用公式，描述了一大类插值方法在希尔伯特空间上的求导算子。它基于一种关于 "临界点 "的简单新技术，在临界点上，所有求导都达到最大值。我们由此推导出此类方法，特别是实数方法的卡尔顿唯一性定理版本。我们的想法的一个应用是构建了一个由实数 J 方法诱导的弱希尔伯特空间。在此之前，人们只知道这种空间产生于复数方法。为了使图景更加完整，我们利用约翰逊和桑科夫斯基的一个突破，展示了其临界点上的值如我们所愿缓慢增长到无穷大的非微分导数。

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A universal formula for derivation operators and applications

We give a universal formula describing derivation operators on a Hilbert space for a large class of interpolation methods. It is based on a simple new technique on “critical points” where all the derivations attain the maximum. We deduce from this a version of Kalton uniqueness theorem for such methods, in particular, for the real method. As an application of our ideas is the construction of a weak Hilbert space induced by the real J-method. Previously, such space was only known arising from the complex method. To complete the picture, we show, using a breakthrough of Johnson and Szankowski, nontrivial derivations whose values on the critical points grow to infinity as slowly as we wish.

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来源期刊

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.