On the diametral dimension of weighted spaces of analytic germs
Volume 233 / 2016
Studia Mathematica 233 (2016), 85-100
MSC: Primary 46A45, 46A63; Secondary 46E10, 46F15, 30H50.
DOI: 10.4064/sm8447-4-2016
Published online: 5 May 2016
Abstract
We prove precise estimates for the diametral dimension of certain weighted spaces of germs of holomorphic functions defined on strips near $\mathbb {R}$. This implies a full isomorphic classification for these spaces including the Gelfand–Shilov spaces $S^1_{\alpha }$ and $S_1^{\alpha }$ for $\alpha \gt 0$. Moreover we show that the classical spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions are not isomorphic.
