The numerical range of holomorphic mappings arises in many aspects of non-linear analysis, finite and infinite dimensional holomorphy, and complex dynamical systems. In particular, this notion plays a crucial role in establishing exponential and product formulas for semigroups of holomorphic mappings, the study of flow invariance and range conditions, geometric function theory in finite and infinite dimensional Banach spaces, and in the study of complete and semi-complete vector fields and their applications to starlike and spirallike mappings, and to Bloch (univalence) radii for locally biholomorphic mappings. In the present paper, we establish lower and upper bounds for the numerical range of holomorphic mappings in Banach spaces. In addition, we study and discuss some geometric and quantitative analytic aspects of fixed point theory, non-linear resolvents of holomorphic mappings, Bloch radii, as well as radii of starlikeness and spirallikeness.

Bracci, F., Levenshtein, M., Reich, S., Shoikhet, D. (2016). Growth Estimates for the Numerical Range of Holomorphic Mappings and Applications. COMPUTATIONAL METHODS AND FUNCTION THEORY, 16(3), 457-487 [10.1007/s40315-015-0155-6].

Growth Estimates for the Numerical Range of Holomorphic Mappings and Applications

Bracci F.
;
2016-01-01

Abstract

The numerical range of holomorphic mappings arises in many aspects of non-linear analysis, finite and infinite dimensional holomorphy, and complex dynamical systems. In particular, this notion plays a crucial role in establishing exponential and product formulas for semigroups of holomorphic mappings, the study of flow invariance and range conditions, geometric function theory in finite and infinite dimensional Banach spaces, and in the study of complete and semi-complete vector fields and their applications to starlike and spirallike mappings, and to Bloch (univalence) radii for locally biholomorphic mappings. In the present paper, we establish lower and upper bounds for the numerical range of holomorphic mappings in Banach spaces. In addition, we study and discuss some geometric and quantitative analytic aspects of fixed point theory, non-linear resolvents of holomorphic mappings, Bloch radii, as well as radii of starlikeness and spirallikeness.
2016
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Numerical range; Growth estimates; Bloch radii; Holomorphic maps; Banach spaces
Bracci, F., Levenshtein, M., Reich, S., Shoikhet, D. (2016). Growth Estimates for the Numerical Range of Holomorphic Mappings and Applications. COMPUTATIONAL METHODS AND FUNCTION THEORY, 16(3), 457-487 [10.1007/s40315-015-0155-6].
Bracci, F; Levenshtein, M; Reich, S; Shoikhet, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/233036
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