TY  - BOOK
AU  - Antoine,Jean-Pierre
AU  - Trapani,Camillo
ED  - SpringerLink (Online service)
TI  - Partial Inner Product Spaces: Theory and Applications 
T2  - Lecture Notes in Mathematics,
SN  - 9783642051364
AV  - QA319-329.9 
U1  - 515.7 23
PY  - 2009///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Functional analysis
KW  - Operator theory
KW  - Functional Analysis
KW  - Operator Theory
KW  - Quantum Field Theories, String Theory
KW  - Information and Communication, Circuits
N1  - General Theory: Algebraic Point of View -- General Theory: Topological Aspects -- Operators on PIP-Spaces and Indexed PIP-Spaces -- Examples of Indexed PIP-Spaces -- Refinements of PIP-Spaces -- Partial *-Algebras of Operators in a PIP-Space -- Applications in Mathematical Physics -- PIP-Spaces and Signal Processing
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-642-05136-4
ER  -