zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Weighted spaces of holomorphic functions on balanced domains. (English) Zbl 0803.46023

This paper deals with radial weights on balanced domains G n , for which it is possible to apply methods involving the Taylor series of holomorphic functions about zero. The contractive properties of the Cesàro means of the Taylor series of functions in the disk algebra are used to derive remarkable consequences for spaces of holomorphic functions on arbitrary balanced open sets in n . This leads to simple proofs that the spaces HV 0 (G) and 𝒱 0 H(G) have the bounded approximation property whenever they contain the polynomials, and that then the polynomials are dense.

The second part of the paper is devoted to a related problem on ε-tensor products with an arbitrary Banach space with applications to certain spaces of vector-valued holomorphic functions. In the last part some remarkable vector-valued generalizations of the (bi- )dualities ((HV 0 (G) b ' ) b ' =HV(G) and ((𝒱 0 H(G)) b ' ) i ' =𝒱H(G) are established.


MSC:
46E10Topological linear spaces of continuous, differentiable or analytic functions
32A07Special domains in n (Reinhardt, Hartogs, circular, tube)
46B28Spaces of operators; tensor products; approximation properties
46M05Tensor products of topological linear spaces