Abstract and Applied Analysis

Metric domains, holomorphic mappings and nonlinear semigroups

Simeon Reich and David Shoikhet

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Abstract

We study nonlinear semigroups of holomorphic mappings on certain domains in complex Banach spaces. We examine, in particular, their differentiability and their representations by exponential and other product formulas. In addition, we also construct holomorphic retractions onto the stationary point sets of such semigroups.

Article information

Source
Abstr. Appl. Anal., Volume 3, Number 1-2 (1998), 203-228.

Dates
First available in Project Euclid: 8 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1049832689

Digital Object Identifier
doi:10.1155/S1085337598000529

Mathematical Reviews number (MathSciNet)
MR1700285

Zentralblatt MATH identifier
0993.47040

Subjects
Primary: 32H15 34G20: Nonlinear equations [See also 47Hxx, 47Jxx] 46G20: Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10] 47H17 47H20: Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07]

Keywords
Banach space Cauchy problem exponential formula holomorphic retraction hyperbolic metric infinitesimal generator nonlinear semigroup product formula resolvent Schwarz-Pick system stationary point set

Citation

Reich, Simeon; Shoikhet, David. Metric domains, holomorphic mappings and nonlinear semigroups. Abstr. Appl. Anal. 3 (1998), no. 1-2, 203--228. doi:10.1155/S1085337598000529. https://projecteuclid.org/euclid.aaa/1049832689


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