Partial Inner Product Spaces Theory and Applications [Paperback]

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

Partial Inner Product Spaces offers a systematic analysis of PIP spaces. Numerous examples are described in detail in addition to applications of PIP spaces in physics and in signal and image processing, respectively.

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

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 andl³;