A characterization of the Schwartz space \(\mathcal S\). (Une caractérisation de l’espace \(\mathcal S\) de Schwartz.) (French) Zbl 0820.46033
Summary: The Schwartz space can be characterized by two separate conditions \(\sup_ x | x^ \beta \varphi(x)|<\infty\), \(\sup_ x | \partial^ \alpha \varphi(x)|< \infty\), and also by the conditions without derivatives \(\sup_ x | x^ \beta \varphi(x)|< \infty\),
\(\sup_ \xi |\xi^ \alpha\widehat \varphi(\xi)|<\infty\).
\(\sup_ \xi |\xi^ \alpha\widehat \varphi(\xi)|<\infty\).
MSC:
| 46F05 | Topological linear spaces of test functions, distributions and ultradistributions |
