Diametral dimension of some pseudoconvex multiscale spaces

• Autorzy: Jean-Marie Aubry , Françoise Bastin
• Języki publikacji: EN

Abstrakty

EN

Stemming from the study of signals via wavelet coefficients, the spaces $S^{ν}$ are complete metrizable and separable topological vector spaces, parametrized by a function ν, 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 ν, $S^{ν}$ 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 $S^{ν}$.

Kategorie tematyczne

• 46A16: Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
• 46A45: Sequence spaces (including K\"othe sequence spaces)
• 46A13: Spaces defined by inductive or projective limits (LB, LF, etc.)
• 46A11: Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 197
• Numer: 1
• Strony: 27-42

Daty

wydano

2010

Twórcy

autor

Jean-Marie Aubry

• Lab. Anal. Math. Appl. (UMR CNRS 8050), Université Paris-Est, 61 av. du Général de Gaulle, F-94010 Créteil, France

autor

Françoise Bastin

• Département de Mathématique (B37), Université de Liège, Grande Traverse, 12, B-4000 Liège, Belgique

Identyfikatory

DOI

10.4064/sm197-1-3