Diametral dimension of some pseudoconvex multiscale spaces
Tom 197 / 2010
Studia Mathematica 197 (2010), 27-42
MSC: 46A16, 46A45, 46A11, 46A13.
DOI: 10.4064/sm197-1-3
Streszczenie
Stemming from the study of signals via wavelet coefficients, the spaces $S^{\nu }$ are complete metrizable and separable topological vector spaces, parametrized by a function $\nu $, whose elements are sequences indexed by a binary tree. Several papers were devoted to their basic topology; recently it was also shown that depending on $\nu $, $S^{\nu }$ may be locally convex, locally $p$-convex for some $p>0$, or not at all, but under a minor condition these spaces are always pseudoconvex. We deal with some more sophisticated properties: their diametral dimensions show that they are Schwartz but not nuclear spaces. Moreover, Ligaud's example of a Schwartz pseudoconvex non-$p$-convex space is actually a particular case of $S^{\nu }$.
