Loewner chains and parametric representation of biholomorphic mappings in complex Banach spaces

Glasnik Matematicki, Vol. 39, No.1 (2004), 55-72.

LOEWNER CHAINS AND PARAMETRIC REPRESENTATION OF BIHOLOMORPHIC MAPPINGS IN COMPLEX BANACH SPACES

Hidetaka Hamada and Gabriela Kohr

Faculty of Engineering, Kyushu Kyoritsu University, 1-8 Jiyugaoka, Yahatanishi-ku, Kitakyushu 807-8585, Japan
e-mail: hamada@kyukyo-u.ac.jp
e-mail: h.hamada@ip.kyusan-u.ac.jp

Faculty of Mathematics, Babes-Bolyai University, 1 M. Kog\u alniceanu Str., Cluj-Napoca, Romania
e-mail: gkohr@math.ubbcluj.ro

Abstract. Let X be a complex Banach space and let B be the unit ball of X. In this paper we obtain sufficient conditions for biholomorphic mappings on B to have parametric representation. Also we study certain properties of Loewner chains, and we obtain infinite dimensional versions of some well known univalence criteria on the unit ball of Cⁿ.

2000 Mathematics Subject Classification. 32H02, 30C45.

Key words and phrases. Biholomorphic mapping, Loewner chains, parametric representation, univalence criteria.

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