報(bào)告題目：Analytic automorphisms, composition operators and the representation of analytic functions
報(bào)告人：侯秉喆教授
報(bào)告時(shí)間：2023.12.7 16：30-17：30
報(bào)告地點(diǎn)：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院 104報(bào)告廳
報(bào)告人簡(jiǎn)介：侯秉喆，于2008年獲得吉林大學(xué)理學(xué)博士學(xué)位，現(xiàn)為吉林大學(xué)數(shù)學(xué)學(xué)院教授，主要從事基礎(chǔ)數(shù)學(xué)的教學(xué)與研究，主要研究方向?yàn)樗阕永碚撆c算子代數(shù)，拓?fù)渑c拓?fù)鋭?dòng)力系統(tǒng)等，在Sci
China Math., Journal of Operator Theory, Proc. Amer. Math. Soc., Topol.
App. 等學(xué)術(shù)期刊發(fā)表論文三十余篇。
報(bào)告內(nèi)容簡(jiǎn)介：In
this talk, we focus on the weighted Hardy spaces of polynomial growth,
which cover the classical Hardy space, weighted Bergman spaces, weighted
Dirichlet spaces and much broader. We discuss the boundedness of the
composition operators with symbols of analytic automorphisms of unit
open disk (finite Blaschke product and analytic functions on the unit
closed disk) acting on weighted Hardy spaces of polynomial growth.
Furthermore, we could compute the K_0-groups of the commutant algebras
of those multiplication operators. Then, the Jordan decomposition
theorem and similar classification for the representation of analytic
functions on the unit closed disk as multiplication operators are
obtained. Moreover, we also study the norms, spectra and
(semi-)Fredholmness of composition operators induced by disc
automorphisms. This is a joint work with Prof. Chunlan Jiang.
