From Besov and modulation spaces to coorbit theory and decomposition spaces
数学专题报告
报告题目(Title)：From Besov and modulation spaces to coorbit theory and decomposition spaces
报告人(Speaker)：Hans Georg Feichtinger教授 （奥地利维也纳大学）
地点(Place)：后主楼 1124
时间(Time)：2024 年 7 月 27 日， 9：00-10：00
邀请人(Inviter)：杨大春、袁文
报告摘要
Both the theory of decomposition spaces (developed together with my PhD student Peter Groebner around 1987) and coorbit theory (developed together with my colleague Karlheinz Groechenig, around 1988-89) provide attempts to generalize the idea of function spaces with some analogy to the theory of Besov spaces.
While decomposition space theory emphasizes the freedome in creating coverings of phase space (uniform for modulation spaces, dyadic rings for Besov spaces, alpha-modulation spaces in between) coorbit theory makes use of the theory of group representations. Modulation spaces relate to the use of time-frequency shifts or the Schroedinger representation of the reduced Heisenberg group, other groups allow similar schemes. Coorbit spaces are also closed under duality and interpolation.
The work of Felix Voigtlaender connects the two approaches, especially with anisotropic wavelet type spaces.
