Семинары: Zh. G. Avetisyan, Mixed-Fourier-norm spaces and holomorphic functions

СЕМИНАРЫ


Seminar on Analysis, Differential Equations and Mathematical Physics 2 октября 2025 г. 18:00, г. Ростов-на-Дону, online

Mixed-Fourier-norm spaces and holomorphic functions Zh. G. Avetisyan Ghent University
Аннотация: We describe a general framework of functional and Fourier analysis on domains with a free action of an Abelian Lie group $G$. Namely, on a domain of the form $G\times Y$ we introduce the appropriate spaces of distributions and measurable functions, establishing their most basic properties. Then we consider the half-Fourier transform $f(x,y)\mapsto\hat f(\xi,y)$ in the first variable, and discuss the behaviour of function spaces on $G\times Y$ and $\hat G\times Y$ under this transform. We introduce general mixed-Fourier-norm spaces on $G\times Y$, and the subspaces of holomorphic functions among them, and give explicit descriptions of the Fourier images of these spaces. Язык доклада: английский Website: https://msrn.tilda.ws/sl