Partial Inner Product Spaces Theory and Applications /

• Main Authors: Antoine, Jean-Pierre (Author), Trapani, Camillo (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Lecture Notes in Mathematics, 1986
• Subjects: Mathematics.; Functional analysis.; Operator theory.; Information theory.; Quantum field theory.; String theory.; Functional Analysis.; Operator Theory.; Quantum Field Theories, String Theory.; Information and Communication, Circuits.
• Physical Description: XX, 358 p. 11 illus. online resource.
• ISBN: 9783642051364
• ISSN: 0075-8434 ;

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.