Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1986)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Partial Inner Product (PIP) Spaces are ubiquitous, e.g. Rigged Hilbert spaces, chains of Hilbert or Banach spaces (such as the Lebesgue spaces Lp over the real line), etc. In fact, most functional spaces used in (quantum) physics and in signal processing are of this type. The book contains a systematic analysis of PIP spaces and operators defined on them. Numerous examples are described in detail and a large bibliography is provided. Finally, the last chapters cover the many applications of PIP spaces in physics and in signal/image processing, respectively.
As such, the book will be useful both for researchers in mathematics and practitioners of these disciplines.
Reviews
From the reviews:
“Partial Inner Product (PIP) spaces generalize and synthesize a lot of spaces appearing in functional analysis, such as rigged Hilbert spaces, scales of Hilbert or Banach spaces, etc. … the book will be of interest for researchers interested in function spaces as well as for those interested in applications in theoretical physics and signal processing.” (Stefan Cobzaş, Zentralblatt MATH, Vol. 1195, 2010)
“The topic of this book is so-called PIP (partial inner product) spaces, which are vector spaces with a symmetric relation on pairs of elements … . Overall the book provides a unique opportunity for researchers working in the field of analysis to take a new perspective on more or less well known families of function spaces or operators, and the common functional analytic features common to all these families, analyzed in a very systematic way. … many readers will enjoy studying the proposed concepts.” (Hans G. Feichtinger, Mathematical Reviews, Issue 2011 i)
Authors and Affiliations
Bibliographic Information
Book Title: Partial Inner Product Spaces
Book Subtitle: Theory and Applications
Authors: Jean-Pierre Antoine, Camillo Trapani
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-642-05136-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2009
Softcover ISBN: 978-3-642-05135-7Published: 04 February 2010
eBook ISBN: 978-3-642-05136-4Published: 08 December 2009
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XX, 358
Number of Illustrations: 11 b/w illustrations
Topics: Functional Analysis, Operator Theory, Quantum Field Theories, String Theory, Information and Communication, Circuits