Simply interpolating sequences in complete Pick spaces

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2024-02-07 DOI:10.1090/tran/9123

Nikolaos Chalmoukis, Alberto Dayan, Michael Hartz

引用次数: 0

Abstract

We characterize simply interpolating sequences (also known as onto interpolating sequences) for complete Pick spaces. We show that a sequence is simply interpolating if and only if it is strongly separated. This answers a question of Agler and M^cCarthy. Moreover, we show that in many important examples of complete Pick spaces, including weighted Dirichlet spaces on the unit disc and the Drury–Arveson space in finitely many variables, simple interpolation does not imply multiplier interpolation. In fact, in those spaces, we construct simply interpolating sequences that generate infinite measures, and uniformly separated sequences that are not multiplier interpolating.

查看原文本刊更多论文

简单插补完整皮克空间中的序列

我们描述了完整皮克空间的简单插值序列（也称为对插值序列）的特征。我们证明，当且仅当一个序列是强分离的时候，它才是简单插值序列。这回答了阿格勒和麦卡锡的一个问题。此外，我们还证明了在完整 Pick 空间的许多重要例子中，包括单位圆盘上的加权 Dirichlet 空间和有限多变量的 Drury-Arveson 空间，简单插值并不意味着乘数插值。事实上，在这些空间中，我们构造了产生无限度量的简单插值序列，以及不是乘数插值的均匀分离序列。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.