论由权重矩阵定义的全局超微分类的包含关系

IF 1.1 3区数学 Q1 MATHEMATICS

Mediterranean Journal of Mathematics Pub Date : 2024-07-08 DOI:10.1007/s00009-024-02694-1

Chiara Boiti, David Jornet, Alessandro Oliaro, Gerhard Schindl

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引用次数: 0

摘要

我们根据定义权重矩阵的增长关系，研究并描述了一般权重矩阵框架中全局类的包含关系。我们考虑了 Roumieu 和 Beurling 两种情况，作为一种特殊情况，我们还处理了经典权重函数和权重序列情况。此外，我们还构建了一个权重序列，它围绕满足某些最小条件的任何权重序列振荡，尤其是围绕临界权重序列 \((p!)^{1/2}\) 振荡，这与类的非琐碎性有关。最后，我们还得到了由权重函数定义的类的比较结果，这些类可以由权重序列定义，反之亦然。

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On the Inclusion Relations of Global Ultradifferentiable Classes Defined by Weight Matrices

We study and characterize the inclusion relations of global classes in the general weight matrix framework in terms of growth relations for the defining weight matrices. We consider the Roumieu and Beurling cases, and as a particular case, we also treat the classical weight function and weight sequence cases. Moreover, we construct a weight sequence which is oscillating around any weight sequence which satisfies some minimal conditions and, in particular, around the critical weight sequence \((p!)^{1/2}\), related with the non-triviality of the classes. Finally, we also obtain comparison results both on classes defined by weight functions that can be defined by weight sequences and conversely.

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来源期刊

Mediterranean Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

261

审稿时长

6-12 weeks

期刊介绍： The Mediterranean Journal of Mathematics (MedJM) is a publication issued by the Department of Mathematics of the University of Bari. The new journal replaces the Conferenze del Seminario di Matematica dell’Università di Bari which has been in publication from 1954 until 2003. The Mediterranean Journal of Mathematics aims to publish original and high-quality peer-reviewed papers containing significant results across all fields of mathematics. The submitted papers should be of medium length (not to exceed 20 printed pages), well-written and appealing to a broad mathematical audience. In particular, the Mediterranean Journal of Mathematics intends to offer mathematicians from the Mediterranean countries a particular opportunity to circulate the results of their researches in a common journal. Through such a new cultural and scientific stimulus the journal aims to contribute to further integration amongst Mediterranean universities, though it is open to contribution from mathematicians across the world.