Vector-valued Modulation Spaces and Localization Operators with Operator-valued Symbols |
| |
Authors: | Patrik Wahlberg |
| |
Institution: | (1) School of Electrical Engineering & Computer Science, The University of Newcastle, Callaghan, NSW, 2308, Australia |
| |
Abstract: | We study the short-time Fourier transformation, modulation spaces, Gabor representations and time-frequency localization operators,
for functions and tempered distributions that have as range space a Banach or a Hilbert space. In the Banach space case the
theory of modulation spaces contains some modifications of the scalar-valued theory, depending on the Banach space. In the
Hilbert space case the modulation spaces have properties similar to the scalar-valued case and the Gabor frame theory essentially
works. For localization operators in this context symbols are operator-valued. We generalize two results from the scalar-valued
theory on continuity on certain modulation spaces when the symbol belongs to an Lp,q space and M∞, respectively. The first result is true for any Banach space as range space, and the second result is true for any Hilbert
space as range space. |
| |
Keywords: | Primary 47G30 42B35 Secondary 47B38 35S99 |
本文献已被 SpringerLink 等数据库收录! |
|