We prove precise estimates for the diametral dimension of certain weighted spaces of germs of holomorphic functions defined on strips near ℝ. This implies a full isomorphic classification for these spaces including the Gelfand-Shilov spaces $S{¹}_{\alpha }$ and $S{₁}^{\alpha }$ for α > 0. Moreover we show that the classical spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions are not isomorphic.

Let ${ℇ}_{\left(\omega \right)}\left(\Omega \right)$ denote the non-quasianalytic class of Beurling type on an open set Ω in ${ℝ}^n$. For $\mu \in {ℇ}_{\left(\omega \right)}^{\text{'}}\left({ℝ}^n\right)$ the surjectivity of the convolution operator $T_{\mu }:{ℇ}_{\left(\omega \right)}\left({\Omega }_1\right)\to {ℇ}_{\left(\omega \right)}\left({\Omega }_2\right)$ is characterized by various conditions, e.g. in terms of a convexity property of the pair $({\Omega }_1,{\Omega }_2)$ and the existence of a fundamental solution for μ or equivalently by a slowly decreasing condition for the Fourier-Laplace transform of μ. Similar conditions characterize the surjectivity of a convolution operator $S_{\mu }:D_{\omega }^{\text{'}}\left({\Omega }_1\right)\to D_{\omega }^{\text{'}}\left({\Omega }_2\right)$ between ultradistributions of Roumieu type whenever $\mu \in {ℇ}_{\omega }^{\text{'}}\left({ℝ}^n\right)$. These...

Si studiano alcune proprietà di un certo limite induttivo di spazi non-archimedei di funzioni continue. In particolare, si esamina la completezza di questo limite induttivo e si indaga il problema di quando lo spazio coincide con il proprio inviluppo proiettivo.

Soit $X$ un espace localement compact. Tout opérateur dissipatif de domaine dense dans $C^0\left(\right(X)$ est limite d’opérateurs dissipatifs bornés. Ce résultat permet, dans le cas où $X$ est un espace homogène, de démontrer que tout opérateur dissipatif, de domaine dense et invariant sur $C^0\left(X\right)$ se prolonge en le générateur infinitésimal d’un semi-groupe à contraction invariant sur $C^0\left(X\right)$.À tout opérateur $A$ vérifiant le principe du maximum positif sur $C^0(X,\mathbf{R})$ et de domaine assez riche, on associe un opérateur bilinéaire $B$, appelé...