Partial Inner Product Spaces

Theory and Applications

  • Jean-Pierre Antoine
  • Camillo Trapani

Part of the Lecture Notes in Mathematics book series (LNM, volume 1986)

Table of contents

  1. Front Matter
    Pages I-XXIX
  2. Jean-Pierre Antoine, Camillo Trapani
    Pages 11-34
  3. Jean-Pierre Antoine, Camillo Trapani
    Pages 35-56
  4. Jean-Pierre Antoine, Camillo Trapani
    Pages 57-101
  5. Jean-Pierre Antoine, Camillo Trapani
    Pages 103-156
  6. Jean-Pierre Antoine, Camillo Trapani
    Pages 157-219
  7. Jean-Pierre Antoine, Camillo Trapani
    Pages 221-255
  8. Jean-Pierre Antoine, Camillo Trapani
    Pages 257-292
  9. Jean-Pierre Antoine, Camillo Trapani
    Pages 293-324
  10. Back Matter
    Pages 325-358

About this book

Introduction

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.

Keywords

Chains of Banach or Hilbert spaces Hilbert space Partial *-algebras of operators Partial inner product spaces linear optimization

Authors and affiliations

  • Jean-Pierre Antoine
    • 1
  • Camillo Trapani
    • 2
  1. 1.Unité de Physique Théorique et deUniversité Catholique de LouvainLeuvenBelgium
  2. 2.Dipto. Matematica ed ApplicazioniUniversità di PalermoPalermoItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-05136-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-05135-7
  • Online ISBN 978-3-642-05136-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book