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Summary: Herbert Amann
Vector-Valued Distributions
and Fourier Multipliers
This manuscript was originally planned to be Chapter VI, that is, the rst chapter
of Volume II of the treatise whose rst volume is [Ama95]. In the meantime I have
changed the concept of that volume and do not plan to include this material. For
this reason, and since some of the results presented here have already been cited
by several authors being in possession of preliminary versions, I have decided to
make it publicly available by putting it on my home page.
Zürich, July 2003
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1 Vector-Valued Distributions
1.1 Locally Convex Topologies . . . . . . . . . . . . . . . . . . . . . . . 2
The Uniform Boundedness Principle . . . . . . . . . . . . . . . . . 3
Hypocontinuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Montel Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Strict Inductive Limits . . . . . . . . . . . . . . . . . . . . . . . . 5
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