解析セミナー Jens Christensen氏

Wavelet theory has been an active area of research
for around 40 years. In this talk we first present a machinery,
called coorbit theory, which uses continuous wavelet transforms
in order to provide atomic decompositions for a large collection of Banach 

spaces. The theory was initiated by Feichtinger and Groechenig,
but we present a recent generalization which is more widely applicable.
Next we present an application to complex analysis.
Due to work by Rudin, Coifman and Rochberg as well as Luecking,
it has long been known that Bergman spaces have atomic decompositions,
where the atoms are samples of the Bergman kernel.
We use coorbit theory to provide a much larger class of atoms
for Bergman spaces on the unit ball.
This class of atoms includes translates of polynomials
under the discrete series representation of SU(n,1).