Locally Convex Spaces over Non-Archimedean Valued Fields
Seiten
2010
Cambridge University Press (Verlag)
978-0-521-19243-9 (ISBN)
Cambridge University Press (Verlag)
978-0-521-19243-9 (ISBN)
This self-contained treatment of the theory of non-Archimedean locally convex spaces provides a clear exposition of the theory, together with complete proofs. A guide to examples and glossary of terms make the book easily accessible to beginners at the graduate level as well as specialists from various disciplines.
Non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. This book is the first to provide a comprehensive treatment of non-Archimedean locally convex spaces. The authors provide a clear exposition of the basic theory, together with complete proofs and new results from the latest research. A guide to the many illustrative examples provided, end-of-chapter notes and glossary of terms all make this book easily accessible to beginners at the graduate level, as well as specialists from a variety of disciplines.
Non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. This book is the first to provide a comprehensive treatment of non-Archimedean locally convex spaces. The authors provide a clear exposition of the basic theory, together with complete proofs and new results from the latest research. A guide to the many illustrative examples provided, end-of-chapter notes and glossary of terms all make this book easily accessible to beginners at the graduate level, as well as specialists from a variety of disciplines.
C. Perez-Garcia is Professor in the Department of Mathematics, Statistics and Computation at the University of Cantabria, Spain. W. H. Schikhof worked as a Professor at Radboud University Nijmegen, Netherlands for forty years. He has since retired but is still active in mathematical research.
Preface; 1. Ultrametrics and valuations; 2. Normed spaces; 3. Locally convex spaces; 4. The Hahn-Banach Theorem; 5. The weak topology; 6. C-compactness; 7. Barrelledness and reflexivity; 8. Montel and nuclear spaces; 9. Spaces with an 'orthogonal' base; 10. Tensor products; 11. Inductive limits; A. Glossary of terms; B. Guide to the examples; Bibliography; Notations; Index.
| Reihe/Serie | Cambridge Studies in Advanced Mathematics |
|---|---|
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 155 x 234 mm |
| Gewicht | 800 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 0-521-19243-9 / 0521192439 |
| ISBN-13 | 978-0-521-19243-9 / 9780521192439 |
| Zustand | Neuware |
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