Weight functions in time-frequency analysis. (English) Zbl 1132.42313
Rodino, Luigi (ed.) et al., Pseudo-differential operators. Partial differential equations and time-frequency analysis. Selected papers of the ISAAC workshop, Toronto, Canada, December 11–15, 2006. Providence, RI: American Mathematical Society (AMS); Toronto: The Fields Institute for Research in Mathematical Sciences (ISBN 978-0-8218-4276-8/hbk). Fields Institute Communications 52, 343-366 (2007).
Summary: We discuss the most common types of weight functions in harmonic analysis and how they occur in time-frequency analysis. As a general rule, submultiplicative weights characterize algebra properties, moderate weights characterize module properties, Gelfand-Raikov-Shilov weights determine spectral invariance, and Beurling-Domar weights guarantee the existence of compactly supported test functions.
For the entire collection see [Zbl 1126.35007].
For the entire collection see [Zbl 1126.35007].
MSC:
| 42C15 | General harmonic expansions, frames |
| 35S05 | Pseudodifferential operators as generalizations of partial differential operators |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 46B15 | Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces |
| 47G30 | Pseudodifferential operators |
| 47B37 | Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) |
