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

  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},
Normal families of holomorphic functions on infinite-dimensional spaces.
The purpose of the present work is to extend some classical results of holomorphic functions of one complex variable to holomorphic functions defined on infinite dimensional spaces. Montel-type and
The Composition Operation on Spaces of Holomorphic Mappings
We discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fr\'{e}chet space of the entire mappings that are bounded on
Holomorphic Dynamics on Bounded Symmetric Domains of Finite Rank.
In this thesis we present new results in holomorphic dynamics on rank-2 bounded symmetric domains, which can be infinite-dimensional. Some of these results have been published in [12]. Together with
Geometrical Analysis in One and Several Complex Variables
Of the topics we initially proposed for study, we spent most of our time considering holomorphic mappings in Banach and Hilbert spaces. Following some early developments dating back to about 1970,
The Carathéodory–Cartan–Kaup–Wu Theorem on an Infinite-Dimensional Hilbert Space
Abstract This paper treats a holomorphic self-mapping f: Ω → Ω of a bounded domain Ω in a separable Hilbert space with a fixed point p. In case the domain is convex, we prove an infinite-dimensional
Wandering Montel Theorems for Hilbert Space Valued Holomorphic Functions
We prove a Montel theorem for Hilbert space valued functions, and a non-commutative version of this theorem, by composing with unitaries to achieve convergence.
Holomorphic shadowing for Hénon maps
We describe a correcting operator for those pseudo-orbits of the quadratic complex Henon map that remain bounded away from the origin by an amount that depends on the map. The iterates of the


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)