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 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.

Summary

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.

Product details

• Authors: J-P Antoine, Camillo Trapani
• Publisher: Springer EN
• Languages: English
• Product format: Paperback / Softback
• Released: 04.02.2010
• EAN: 9783642051357
• ISBN: 978-3-642-05135-7
• No. of pages: 358
• Weight: 1170 g
• Illustrations: XX, 358 p. 11 illus., schwarz-weiss Illustrationen
• Series: Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; B, Mathematics and Statistics, String Theory, Mathematical Applications in Computer Science, Functional Analysis, Quantum field theory, Elementary Particles, Quantum Field Theory, Information theory, Applied mathematics, Functional analysis & transforms, Operator Theory, Statistical physics, Information and Communication, Circuits, Quantum Field Theories, String Theory