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.
Author(s): Jean-Pierre Antoine, Camillo Trapani (auth.)
Series: Lecture Notes in Mathematics 1986
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2009
Language: English
Pages: 358
Tags: Functional Analysis;Operator Theory;Quantum Field Theories, String Theory;Information and Communication, Circuits
Front Matter....Pages I-XXIX
General Theory: Algebraic Point of View....Pages 11-34
General Theory: Topological Aspects....Pages 35-56
Operators on PIP-Spaces and Indexed PIP-Spaces....Pages 57-101
Examples of Indexed PIP-Spaces....Pages 103-156
Refinements of PIP-Spaces....Pages 157-219
Partial *-Algebras of Operators in a PIP-Space....Pages 221-255
Applications in Mathematical Physics....Pages 257-292
PIP-Spaces and Signal Processing....Pages 293-324
Back Matter....Pages 325-358
