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Published in:
2010 | OriginalPaper | Chapter
Appendix
Author : Nicolas Lerner
Published in: Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators
Publisher: Birkhäuser Basel
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Let
n
≥1 be an integer. The Schwartz space
S
(ℝ
n
) is defined as the space of
C
∞
functions
u
from ℝ
n
to ℂ such that, for all multi-indices
1
α, β∈ℕ
n
,
$$ \mathop {\sup }\limits_{x \in \mathbb{R}^n } \left| {x^\alpha \partial _x^\beta u(x)} \right| < + \infty . $$