Partial Inner Product Spaces : Theory and Applications

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...

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Main Authors: Antoine, J-P., Trapani, Camillo (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2009, 2009
Edition:1st ed. 2009
Series:Lecture Notes in Mathematics
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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245 0 0 |a Partial Inner Product Spaces  |h Elektronische Ressource  |b Theory and Applications  |c by J-P Antoine, Camillo Trapani 
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505 0 |a 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 #x002A;-Algebras of Operators in a PIP-Space -- Applications in Mathematical Physics -- PIP-Spaces and Signal Processing 
653 |a String theory 
653 |a Functional analysis 
653 |a Functional Analysis 
653 |a Quantum field theory 
653 |a Information and Communication, Circuits 
653 |a Operator Theory 
653 |a Information theory 
653 |a Operator theory 
653 |a Quantum Field Theories, String Theory 
700 1 |a Trapani, Camillo  |e [author] 
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520 |a 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