Quantum normal families: normal families of holomorphic functions and mappings on a Banach space

@article{Kim2002QuantumNF,
  title={Quantum normal families: normal families of holomorphic functions and mappings on a Banach space},
  author={Kang-Tae Kim and Steven G. Krantz},
  journal={arXiv: Complex Variables},
  year={2002}
}
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References

SHOWING 1-10 OF 64 REFERENCES
Weak-type normal families of holomorphic mappings in Banach spaces and characterization of the Hilbert ball by its automorphism group
We present a characterization of the open unit ball in a separable infinite dimensional Hilbert space by the property of automorphism orbits among the domains that are not necessarily bounded. This
Normal Families of Meromorphic Functions
Basic notions and theorems criteria of normality of families of holomorphic functions and applications criteria of normality of families of meromorphic functions and applications closed families of
Weighted spaces of holomorphic functions on Banach spaces
In this paper we study composition operators between weighted spaces of holomorphic functions defined on the open unit ball of a Banach space. Necessary and sufficient conditions are given for
On types of polynomials and holomorphic functions on Banach spaces
In 1966 L. Nachbin introduced the notion of a holomorphy type to consider certain types of polynomials (f.i. compact, nuclear, absolutely summing) in a uniform way [7,8].Holomorphy types with special
Surjective limits of locally convex spaces and their application to infinite dimensional holomorphy
— A locally convex space, F, is a surjective limit of the locally convex spaces, (Ea) ^ . if there exists, for each a in A, a continuous linear mapping. Tin, from E onto Ea and the inverse images of
On some various notions of infinite dimensional holomorphy
The aim of the present work is to show that many notions of holomorphic maps in the framework of locally convex spaces (l.c.s.) or bornological vector spaces (b.v.s.) are in fact reducible to only
Monomial Expansions in Infinite Dimensional Holomorphy
Let E and F denote locally convex spaces over C and let U denote an open subset of E. A function f: U→F is called holomorphic if a it is continuous, b. for each a ∈ U, υ ∈ E and \(
Normal families: New perspectives
This paper surveys some surprising applications of a lemma characterizing normal families of meromorphic functions on plane domains. These include short and efficient proofs of generalizations of (i)
...
...