Search results for "Identity theorem"

showing 2 items of 12 documents

Group-symmetric holomorphic functions on a Banach space

2016

We study the holomorphic functions on a complex Banach space E that are invariant under the action of a given group of operators on E. A great variety of situations occur depending, of course, on the group and the space. Nevertheless, in the examples we deal with, they can be described in terms of a few natural ones and functions of a finite number of variables. Fil: Aron, Richard. Universidad de Valencia; España Fil: Galindo, Pablo. Universidad de Valencia; España Fil: Pinasco, Damian. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Zalduendo, Ignacio Martin. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de I…

Pure mathematicsMatemáticasGeneral MathematicsSymmetric holomorphic functions010102 general mathematicsInfinite-dimensional vector functionHolomorphic functional calculusMathematical analysis//purl.org/becyt/ford/1.1 [https]Banach manifoldInfinite-dimensional holomorphyIdentity theorem01 natural sciencesMatemática Pura//purl.org/becyt/ford/1 [https]010101 applied mathematicsBergman spaceInterpolation spaceAnalyticity of holomorphic functions0101 mathematicsCIENCIAS NATURALES Y EXACTASMathematics
researchProduct

Holomorphic approximation of ultradifferentiable functions

1981

Introduct ion Let S be a closed subset of some open set in Cn and denote by dT(S) the space of germs of holomorphic functions on (a neighborhood of) S. For a space F(S) of tEvalued (continuous, differentiable etc.) functions on S [containing t~(S)] the problem of holomorphic approximation consists of finding conditions to ensure that the natural mapping Q : e)(S)-~F(S) has dense range with respect to a given topology on F(S). Positive solutions for F = C r, 0_ l . For Q:tP(/3)~O(D)c~C(/3), DCIE n strongly pseudoconvex, proofs were given independently by Henkin [17], Kerzman [21], and Lieb [27], for the case e : (9(/3)~(9(D)c~C~(/3) cf. also [30] and for Sobolev spaces see Bell [3, Sect. 6].…

Sobolev spaceSequencePure mathematicsMathematics::Complex VariablesGeneral MathematicsMathematical analysisHolomorphic functionOpen setFunction (mathematics)Differentiable functionIdentity theoremSpace (mathematics)MathematicsMathematische Annalen
researchProduct