An Introduction to the Theory of Multipliers

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...

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Main Author: Larsen, Ronald
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1971, 1971
Edition:1st ed. 1971
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 0. Prologue: The Multipliers for L1(G)
  • 0.0. Introduction
  • 0.1. Multipliers for L1(G)
  • 0.2. Notation
  • 0.3. Notes
  • 1. The General Theory of Multipliers
  • 1.0. Introduction
  • 1.1. Elementary Theory of Multipliers
  • 1.2. Characterizations of Multipliers
  • 1.3. An Application: Multiplications which Preserve the Regular Maximal Ideals
  • 1.4. Maximal Ideal Spaces
  • 1.5. Integral Representations of Multipliers
  • 1.6. Isometric Multipliers
  • 1.7. Multipliers and Dual Spaces
  • 1.8. The Derived Algebra
  • 1.9. The Derived Algebra for Lp(G), 1? p M(Lp(G), Lq(G)), l?p, q??
  • 5.5. Some Results Concerning Lp(G) and M(Lp(G), Lq(G))
  • 5.6. M(Lp(G), Lq(G)) as a Dual Space, 1?p, q??
  • 5.7. Multipliers with Small Support
  • 5.8. Notes
  • 6. The Multipliers for Functions with Fourier Transforms in Lp (?)
  • 6.0. Introduction
  • 6.1. The Banach Algebras Ap(G)
  • 6.2. The Multipliers for Ap(G) as Pseudomeasures
  • 6.3. The Multipliers for Ap(G): G Noncompact
  • 6.4. The Multipliers for Ap(G): G Compact
  • 6.5. Notes
  • 7. The Multipliers for the Pair (Hp(G), Hq (G)), 1?p, q??
  • 7.0. Introduction
  • 7.1. General Properties of M(Hp(G), Hq (G)), 1?p, q??
  • 7.2. The Multipliers for the Pair (Hp(G), Hq (G)), 1?q?2?p??
  • 7.3. The Multipliers for the Pair (Hp(G), H?(G)), 1?p??
  • 7.4. Notes
  • Appendices
  • Appendix A: Topology
  • Appendix B: Topological Groups
  • Appendix C: Measure and Integration
  • Appendix D: Functional Analysis
  • Appendix E: Banach Algebras
  • Appendix F: Harmonic Analysis
  • Author and Subject Index