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VOL. 44 | 2006 A decomposition of the Schwartz class by a derivative space and its complementary space
Takahide Kurokawa

Editor(s) Hiroaki Aikawa, Takashi Kumagai, Yoshihiro Mizuta, Noriaki Suzuki

## Abstract

Let $\mathcal{D} (R^n)$ be the class of all $C^{\infty}$–functions on $R^n$ with compact support. For a multi-index $\alpha$ we denote $\mathcal{D}^{\alpha} (R^n) = \{\mathcal{D}^{\alpha} \varphi : \varphi \in \mathcal{D} (R^n)\}$. We give a direct sum decomposition of $\mathcal{D} (R^n)$ by $\mathcal{D}^{\alpha} (R^n)$ and its complementary space.

## Information

Published: 1 January 2006
First available in Project Euclid: 16 December 2018

zbMATH: 1118.46037
MathSciNet: MR2277832

Digital Object Identifier: 10.2969/aspm/04410179

Subjects:
Primary: 46E10