Si K es un compacto no vacío en Rr, damos una condición suficiente para que la inyección canónica de ε{M},b(K) en ε{M},d(K) sea nuclear. Consideramos el caso mixto y obtenemos la existencia de un operador de extensión nuclear de ε{M1}(F)A en ε{M2}(Rr)D donde F es un subconjunto cerrado propio de Rr y A y D son discos de Banach adecuados. Finalmente aplicamos este último resultado al caso Borel, es decir cuando F = {0}.

Let K be a compact set in ℂ, f a function analytic in ℂ̅∖K vanishing at ∞. Let $f\left(z\right)={\sum }_{k=0}^{\infty }{a}_k{z}^{-k-1}$ be its Taylor expansion at ∞, and $H_s\left(f\right)=det{\left(a_{k+l}\right)}_{k,l=0}^s$ the sequence of Hankel determinants. The classical Pólya inequality says that $limsu{p}_{s\to \infty }{\left|H_s\left(f\right)\right|}^{1/s²}\le d\left(K\right)$, where d(K) is the transfinite diameter of K. Goluzin has shown that for some class of compacta this inequality is sharp. We provide here a sharpness result for the multivariate analog of Pólya’s inequality, considered by the second author in Math. USSR Sbornik 25 (1975), 350-364.

In this paper, we establish some density theorems in the setting of particular locally convex vector lattices of continuous functions de ned on a locally compact Hausdorff space, which we introduced and studied in [3,4] and which we named regular vector lattices. In this framework, by using properties of the subspace of the so-called generalized af ne functions, we give a simple description of the closed vector sublattice, the closed Stone vector sublattice and the closed subalgebra generated by...

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.