National Institute of the Republic of Serbia
ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζωῶν τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν
PROGRAM
| ODELJENJE ZA MATEMATIKU MATEMATIČKOG INSTITUTA SANU |
PROGRAM ZA MART 2017.
PETAK, 17.03.2017. u 14:15, Sala 301f, MI SANU, Kneza Mihaila 36
Hans G. Feichtinger, University of Vienna, Austria
FOURIER STANDARD SPACES: A NEW FAMILY OF FUNCTION SPACES
Classical Harmonic Analysis is focusing very much on the
Lebesgue spaces $L^1,L^2,L^\infty$, because they appear at first sight as
natural domains for convolution or the Fourier transform. As it has turned
out a variant of distribution theory, arising from problems in
time-frequency analysis, gives rise the a description of the Fourier
transform as an automorphism of the Banach Gelfand Triple (or rigged
Hilbert space) $(S_0,L^2,S_0')(R^d)$, i.e. the Plancherel theorem
restricts well to the space of test functions $S_0(R^d)$ but also extends
well to the distibutions in $S_0'(R^d)$, including Dirac measures, Dirac
combs, or pure frequencies.
Fourier standard spaces is a family of Banach spaces between $S_0(R^d)$
and $S_0'(R^d)$, with some extra properties, essentially allowing
smoothing (by convolution) and localization (by pointwise multiplication).
It is the purpose of this talk to indicate the richness of this family of
Fourier standard spaces, among them Wiener amalgam spaces or modulation
spaces, and to present a few general claims which can be made for the
Banach spaces in this family. Of course, the classical $L^p$-spaces belong
to this family, however without playing a significant role there.