We prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient spaces, thus extending the previous work by Langenbruch. As a consequence, we give very general conditions for these spaces to be nuclear. In particular, we obtain the corresponding results for spaces defined by weight functions.
Download full-text PDF |
Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7594626 | PMC |
| http://dx.doi.org/10.1007/s43037-020-00090-x | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
On Orlicz classes defined in terms of associated weight functions.
Mon Hefte Math
May 2024
Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.
N-functions and their growth and regularity properties are crucial in order to introduce and study Orlicz classes and Orlicz spaces. We consider N-functions which are given in terms of so-called associated weight functions. These functions are frequently appearing in the theory of ultradifferentiable function classes and in this setting additional information is available since associated weight functions are defined in terms of a given weight sequence.
View Article and Find Full Text PDFOn the Inclusion Relations of Global Ultradifferentiable Classes Defined by Weight Matrices.
Mediterr J Math
July 2024
Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz n. 1, 1090 Wien, Austria.
Article Synopsis
- The study explores the relationships between global classes within a weight matrix framework, focusing on how growth relations of weight matrices affect inclusion relations.
- The researchers analyze both Roumieu and Beurling cases, and also examine classical weight functions and sequences as specific examples.
- They create a new oscillating weight sequence that aligns with critical conditions and derive comparison results between classes formed by weight functions and those formed by weight sequences.
Ultradifferentiable classes of entire functions.
Adv Oper Theory
September 2023
Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.
We study classes of ultradifferentiable functions defined in terms of small weight sequences violating standard growth and regularity requirements. First, we show that such classes can be viewed as weighted spaces of entire functions for which the crucial weight is given by the associated weight function of the so-called conjugate weight sequence. Moreover, we generalize results from M.
View Article and Find Full Text PDFNuclear global spaces of ultradifferentiable functions in the matrix weighted setting.
Banach J Math Anal
October 2020
Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz n. 1, 1090 Wien, Austria.
We prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient spaces, thus extending the previous work by Langenbruch. As a consequence, we give very general conditions for these spaces to be nuclear. In particular, we obtain the corresponding results for spaces defined by weight functions.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!