Displaying similar documents to “Metric domains, holomorphic mappings and nonlinear semigroups.”

Semigroups and generators on convex domains with the hyperbolic metric

Simeon Reich, David Shoikhet (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Let D be domain in a complex Banach space X , and let ρ be a pseudometric assigned to D by a Schwarz-Pick system. In the first section of the paper we establish several criteria for a mapping f : D → X to be a generator of a ρ -nonexpansive semigroup on D in terms of its nonlinear resolvent. In the second section we let X = H be a complex Hilbert space, D = B the open unit ball of H , and ρ the hyperbolic metric on B . We introduce the notion of a ρ -monotone mapping and obtain simple characterizations of...

Averages of holomorphic mappings and holomorphic retractions on convex hyperbolic domains

Simeon Reich, David Shoikhet (1998)

Studia Mathematica

Similarity:

Let D be a hyperbolic convex domain in a complex Banach space. Let the mapping F ∈ Hol(D,D) be bounded on each subset strictly inside D, and have a nonempty fixed point set ℱ in D. We consider several methods for constructing retractions onto ℱ under local assumptions of ergodic type. Furthermore, we study the asymptotic behavior of the Cesàro averages of one-parameter semigroups generated by holomorphic mappings.

Holomorphic semigroups of holomorphic isometries

Edoardo Vesentini (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

A previous paper was devoted to the construction of non-trivial holomorphic families of holomorphic isometries for the Carathéodory metric of a bounded domain in a complex Banach space, fixing a point in the domain. The present article shows that such a family cannot exist if it contains a strongly continuous one parameter semigroup.

Holomorphic semigroups of holomorphic isometries

Edoardo Vesentini (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

A previous paper was devoted to the construction of non-trivial holomorphic families of holomorphic isometries for the Carathéodory metric of a bounded domain in a complex Banach space, fixing a point in the domain. The present article shows that such a family cannot exist if it contains a strongly continuous one parameter semigroup.

Lineability of the set of holomorphic mappings with dense range

Jerónimo López-Salazar (2012)

Studia Mathematica

Similarity:

Let U be an open subset of a separable Banach space. Let ℱ be the collection of all holomorphic mappings f from the open unit disc 𝔻 ⊂ ℂ into U such that f(𝔻) is dense in U. We prove the lineability and density of ℱ in appropriate spaces for different choices of U.

The Łojasiewicz exponent of c-holomorphic mappings

Maciej P. Denkowski (2005)

Annales Polonici Mathematici

Similarity:

The aim of this paper is to study the Łojasiewicz exponent of c-holomorphic mappings. After introducing an order of flatness for c-holomorphic mappings we give an estimate of the Łojasiewicz exponent in the case of isolated zero, which is a generalization of the one given by Płoski and earlier by Chądzyński for two variables.

Extending holomorphic maps in infinite dimensions

Bui Dac Tac (1991)

Annales Polonici Mathematici

Similarity:

Studying the sequential completeness of the space of germs of Banach-valued holomorphic functions at a points of a metric vector space some theorems on extension of holomorphic maps on Riemann domains over topological vector spaces with values in some locally convex analytic spaces are proved. Moreover, the extendability of holomorphic maps with values in complete C-spaces to the envelope of holomorphy for the class of bounded holomorphic functions is also established. These results...