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On the Inclusion Relations of Global Ultradifferentiable Classes Defined by Weight Matrices
Chiara Boiti1, David Jornet2, Alessandro Oliaro3
1Dipartimento di Matematica e Informatica, Università di Ferrara, Via Machiavelli n. 30, 44121 Ferrara, Italy.
Mediterranean Journal of Mathematics
|July 11, 2024
Summary
This study analyzes global classes within the weight matrix framework, detailing their inclusion relationships based on growth properties. It introduces a novel oscillating weight sequence and compares function and sequence-defined classes.
Area of Science:
- Mathematical Analysis
- Functional Analysis
- Abstract Algebra
Background:
- The study of global classes in analysis is crucial for understanding function spaces.
- Weight matrices provide a general framework for defining and analyzing these classes.
- Previous work has focused on specific cases like Roumieu and Beurling classes.
Purpose of the Study:
- To characterize inclusion relations of global classes using growth relations of defining weight matrices.
- To investigate these relations within the Roumieu and Beurling frameworks.
- To explore the interplay between weight functions and weight sequences.
Main Methods:
- Analysis of growth relations for weight matrices.
- Construction of a specific oscillating weight sequence.
- Comparison of classes defined by weight functions and weight sequences.
Main Results:
- Established inclusion relations for global classes based on weight matrix growth.
- Developed a new weight sequence oscillating around critical sequences like (p!)^(1/2).
- Demonstrated comparability between weight function-defined and weight sequence-defined classes.
Conclusions:
- The growth relations of weight matrices effectively determine inclusion properties of global classes.
- The constructed oscillating weight sequence offers new tools for analysis.
- A unified understanding between weight function and weight sequence approaches is achieved.
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