The Partial Inner Product Space Method : A Quick Overview
Joint Authors
Antoine, Jean-Pierre
Trapani, Camillo
Source
Advances in Mathematical Physics
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-37, 37 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-07-04
Country of Publication
Egypt
No. of Pages
37
Main Subjects
Abstract EN
Many families of function spaces play a central role in analysis, in particular, in signal processing (e.g., wavelet or Gabor analysis).
Typical are Lp spaces, Besov spaces, amalgam spaces, or modulation spaces.
In all these cases, the parameter indexing the family measures the behavior (regularity, decay properties) of particular functions or operators.
It turns out that all these space families are, or contain, scales or lattices of Banach spaces, which are special cases of partial inner product spaces (PIP-spaces).
In this context, it is often said that such families should be taken as a whole and operators, bases, and frames on them should be defined globally, for the whole family, instead of individual spaces.
In this paper, we will give an overview of PIP-spaces and operators on them, illustrating the results by space families of interest in mathematical physics and signal analysis.
The interesting fact is that they allow a global definition of operators, and various operator classes on them have been defined.Erratum to “The Partial Inner Product Space Method: A Quick Overview”dx.doi.org/10.1155/2011/272703
American Psychological Association (APA)
Antoine, Jean-Pierre& Trapani, Camillo. 2010. The Partial Inner Product Space Method : A Quick Overview. Advances in Mathematical Physics،Vol. 2010, no. 2010, pp.1-37.
https://search.emarefa.net/detail/BIM-473061
Modern Language Association (MLA)
Antoine, Jean-Pierre& Trapani, Camillo. The Partial Inner Product Space Method : A Quick Overview. Advances in Mathematical Physics No. 2010 (2010), pp.1-37.
https://search.emarefa.net/detail/BIM-473061
American Medical Association (AMA)
Antoine, Jean-Pierre& Trapani, Camillo. The Partial Inner Product Space Method : A Quick Overview. Advances in Mathematical Physics. 2010. Vol. 2010, no. 2010, pp.1-37.
https://search.emarefa.net/detail/BIM-473061
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-473061