Partial Inner Product Spaces

Theory and Applications
Erscheinungsjahr 2010
ISBN: 978-3-642-05135-7
Verlag: Springer

Buch, Englisch, 358 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1170 g

Reihe: Lecture Notes in Mathematics

Partial Inner Product (PIP) Spaces are ubiquitous, e.g. Rigged Hilbert spaces, chains of Hilbert or Banach spaces (such as the Lebesgue spaces L 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.

Zielgruppe

Research

Autoren/Hrsg.

Antoine, J-P

Trapani, Camillo

Fachgebiete

• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Informationstheorie, Kodierungstheorie
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme

Inhaltsverzeichnis

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.