Overview
- Presents spectral theory in the non-Archimedean setting; useful to physicists and theoretically-oriented engineers
- Details fundamental material which renders a useful reference for students and researchers
- Useful for independent study or seminar use
- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book focuses on the theory of linear operators on non-Archimedean Banach spaces. The topics treated in this book range from a basic introduction to non-Archimedean valued fields, free non-Archimedean Banach spaces, bounded and unbounded linear operators in the non-Archimedean setting, to the spectral theory for some classes of linear operators. The theory of Fredholm operators is emphasized and used as an important tool in the study of the spectral theory of non-Archimedean operators. Explicit descriptions of the spectra of some operators are worked out. Moreover, detailed background materials on non-Archimedean valued fields and free non-Archimedean Banach spaces are included for completeness and for reference.
The readership of the book is aimed toward graduate and postgraduate students, mathematicians, and non-mathematicians such as physicists and engineers who are interested in non-Archimedean functional analysis. Further,it can be used as an introduction to the study of non-Archimedean operator theory in general and to the study of spectral theory in other special cases.
Reviews
“This book presents some of the authors’ recent work on continuous linear operators on non-archimedean Banach space as well as their spectral theory. … The book can be recommended to beginners as an introduction to non-archimendean operator theory.” (Bertin Diarra, Mathematical Reviews, January, 2017)
“The book is intended as an introduction to the non-Archimedean operator theory ‘for graduate and postgraduate students, mathematicians, and non-mathematicians such as physicists and engineers who are interested in functional analysis in the non-Archimedean context’. Of course, expecting the readership being so wide, the authors make the exposition as elementary as possible.” (Anatoly N. Kochubei, zbMATH 1357.47002, 2017)
Authors and Affiliations
Bibliographic Information
Book Title: Non-Archimedean Operator Theory
Authors: Toka Diagana, François Ramaroson
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-27323-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2016
Softcover ISBN: 978-3-319-27322-8Published: 15 April 2016
eBook ISBN: 978-3-319-27323-5Published: 07 April 2016
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: XIII, 156
Topics: Operator Theory, Functional Analysis, Field Theory and Polynomials, Real Functions