Partial Inner Product Spaces Theory and Applications /

• Main Authors: Antoine, Jean-Pierre. (Author), Trapani, Camillo. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Lecture Notes in Mathematics, 1986
• Subjects: Mathematics.; Functional analysis.; Operator theory.; Functional Analysis.; Operator Theory.; Quantum Field Theories, String Theory.; Information and Communication, Circuits.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-05136-4

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 systema...

Table of Contents:

• 1 General Theory : Algebraic Point of View
• 2 General Theory : Topological Aspects
• 3 Operators on PIP-spaces and Indexed PIP-spaces
• 4 Examples of Indexed PIP-spaces
• 5 Refinements of PIP-spaces
• 6 Partial *-algebras of Operators in a PIP-space
• 7 Applications in Mathematical Physics
• 8 PIP-spaces and Signal Processing.