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august 2015 The convenient setting for ultradifferentiable mappings of Beurling- and Roumieu-type defined by a weight matrix
Gerhard Schindl
Bull. Belg. Math. Soc. Simon Stevin 22(3): 471-510 (august 2015). DOI: 10.36045/bbms/1442364593

Abstract

We prove in a uniform way that all ultradifferentiable function classes $\mathcal{E}_{\{\mathcal{M}\}}$ of Roumieu-type and $\mathcal{E}_{(\mathcal{M})}$ of Beurling-type defined in terms of a weight matrix $\mathcal{M}$ admit a convenient setting if $\mathcal{M}$ satisfies some mild regularity conditions. For $\mathcal{C}$ denoting either $\mathcal{E}_{\{\mathcal{M}\}}$ or $\mathcal{E}_{(\mathcal{M})}$ the category $\mathcal{C}$ is cartesian closed, i.e. $\mathcal{C}(E\times F,G)\cong\mathcal{C}(E,\mathcal{C}(F,G))$ for $E,F,G$ convenient vector spaces. As special cases one obtains the classes $\mathcal{E}_{\{M\}}$ and $\mathcal{E}_{(M)}$ respectively $\mathcal{E}_{\{\omega\}}$ and $\mathcal{E}_{(\omega)}$ defined by a weight sequence $M$ respectively a weight function $\omega$.

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Gerhard Schindl. "The convenient setting for ultradifferentiable mappings of Beurling- and Roumieu-type defined by a weight matrix." Bull. Belg. Math. Soc. Simon Stevin 22 (3) 471 - 510, august 2015. https://doi.org/10.36045/bbms/1442364593

Information

Published: august 2015
First available in Project Euclid: 16 September 2015

zbMATH: 1337.46020
MathSciNet: MR3396997
Digital Object Identifier: 10.36045/bbms/1442364593

Subjects:
Primary: 46E10 , 46T05‎ , 46T10

Keywords: convenient setting , ultradifferentiable functions

Rights: Copyright © 2015 The Belgian Mathematical Society

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Vol.22 • No. 3 • august 2015
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