Ebook: An Introduction to the Theory of Multipliers
Author: Professor Ronald Larsen (auth.)
- Tags: Mathematics general
- Series: Die Grundlehren der mathematischen Wissenschaften 175
- Year: 1971
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
When I first considered writing a book about multipliers, it was my intention to produce a moderate sized monograph which covered the theory as a whole and which would be accessible and readable to anyone with a basic knowledge of functional and harmonic analysis. I soon realized, however, that such a goal could not be attained. This realization is apparent in the preface to the preliminary version of the present work which was published in the Springer Lecture Notes in Mathematics, Volume 105, and is even more acute now, after the revision, expansion and emendation of that manuscript needed to produce the present volume. Consequently, as before, the treatment given in the following pages is eclectric rather than definitive. The choice and presentation of the topics is certainly not unique, and reflects both my personal preferences and inadequacies, as well as the necessity of restricting the book to a reasonable size. Throughout I have given special emphasis to the func tional analytic aspects of the characterization problem for multipliers, and have, generally, only presented the commutative version of the theory. I have also, hopefully, provided too many details for the reader rather than too few.
Content:
Front Matter....Pages N3-XXI
Prologue: The Multipliers for L 1(G)....Pages 1-12
The General Theory of Multipliers....Pages 13-60
The Multipliers for Commutative H*-Algebras....Pages 61-65
Multipliers for Topological Linear Spaces of Functions and Measures....Pages 66-90
The Multipliers for L p (G)....Pages 91-133
The Multipliers for the Pair (L p (G), L q (G)), 1 ? p, q ? ?....Pages 134-194
The Multipliers for Functions with Fourier Transforms in L p (?)....Pages 195-217
The Multipliers for the Pair (H p (G), H q (G)),1 ? p, q ? ?....Pages 218-224
Back Matter....Pages 225-284
Content:
Front Matter....Pages N3-XXI
Prologue: The Multipliers for L 1(G)....Pages 1-12
The General Theory of Multipliers....Pages 13-60
The Multipliers for Commutative H*-Algebras....Pages 61-65
Multipliers for Topological Linear Spaces of Functions and Measures....Pages 66-90
The Multipliers for L p (G)....Pages 91-133
The Multipliers for the Pair (L p (G), L q (G)), 1 ? p, q ? ?....Pages 134-194
The Multipliers for Functions with Fourier Transforms in L p (?)....Pages 195-217
The Multipliers for the Pair (H p (G), H q (G)),1 ? p, q ? ?....Pages 218-224
Back Matter....Pages 225-284
....