Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: spaces of analytic functions

Sortuj według:

Ogranicz wyniki do:

Interpolation d'opérateurs entre espaces de fonctions holomorphes

100%

Lassere P.

Annales Polonici Mathematici

1991-1992

tom 56

nr 1

97-102

Let $K$ be a compact subset of an hyperconvex open set $D ⊂ ℂ^n$, forming with D a Runge pair and such that the extremal p.s.h. function ω(·,K,D) is continuous. Let H(D) and H(K) be the spaces of holomorphic functions respectively on D and K equipped with their usual topologies. The main result of this paper contains as a particular case the following statement: if T is a continuous linear map of H(K) into H(K) whose restriction to H(D) is continuous into H(D), then the restriction of T to $H(D_α)$ is a continuous linear map of $H(D_α)$ into $H(D_α)$, ∀α ∈ ]0,1[ where $D_α = {z ∈ D : ω(z,D,K) < α}$.

Operators on spaces of analytic functions

88%

Seddighi K.

Studia Mathematica

1994

tom 108

nr 1

49-54

Let $M_z$ be the operator of multiplication by z on a Banach space of functions analytic on a plane domain G. We say that $M_z$ is polynomially bounded if $∥M_p∥ ≤ C∥p∥_G$ for every polynomial p. We give necessary and sufficient conditions for $M_z$ to be polynomially bounded. We also characterize the finite-codimensional invariant subspaces and derive some spectral properties of the multiplication operator in case the underlying space is Hilbert.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Studia Mathematica

1 Lassere P.

1 Seddighi K.

1 1994

1 1991

Wyniki wyszukiwania

Interpolation d'opérateurs entre espaces de fonctions holomorphes

Operators on spaces of analytic functions