Antoine, Jean-Pierre.
Partial Inner Product Spaces Theory and Applications / [electronic resource] : by Jean-Pierre Antoine, Camillo Trapani. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2009. - XX, 358 p. 11 illus. online resource. - Lecture Notes in Mathematics, 1986 0075-8434 ; . - Lecture Notes in Mathematics, 1986 .
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.
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.
9783642051364
10.1007/978-3-642-05136-4 doi
Mathematics.
Functional analysis.
Operator theory.
Mathematics.
Functional Analysis.
Operator Theory.
Quantum Field Theories, String Theory.
Information and Communication, Circuits.
QA319-329.9
515.7
Partial Inner Product Spaces Theory and Applications / [electronic resource] : by Jean-Pierre Antoine, Camillo Trapani. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2009. - XX, 358 p. 11 illus. online resource. - Lecture Notes in Mathematics, 1986 0075-8434 ; . - Lecture Notes in Mathematics, 1986 .
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.
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.
9783642051364
10.1007/978-3-642-05136-4 doi
Mathematics.
Functional analysis.
Operator theory.
Mathematics.
Functional Analysis.
Operator Theory.
Quantum Field Theories, String Theory.
Information and Communication, Circuits.
QA319-329.9
515.7