On the construction of large Algebras not contained in the image of the Borel map
| Autor: | Esser, Céline, Schindl, Gerhard |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Res. Math. 75, no. 22, 2020 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00025-019-1146-0 |
| Popis: | The Borel map $j^{\infty}$ takes germs at 0 of smooth functions to the sequence of iterated partial derivatives at 0. It is well known that the restriction of $j^{\infty}$ to the germs of quasianalytic ultradifferentiable classes which are strictly containing the real analytic functions can never be onto the corresponding sequence space. In a recent paper the authors have studied the size of the image of $j^{\infty}$ by using different approaches and worked in the general setting of quasianalytic ultradifferentiable classes defined by weight matrices. The aim of this paper is to show that the image of $j^{\infty}$ is also small with respect to the notion of algebrability and we treat both the Cauchy product (convolution) and the pointwise product. In particular, a deep study of the stability of the considered spaces under the pointwise product is developed. Comment: 30 pages; this version has been accepted for publication in Res. Math |
| Databáze: | arXiv |
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