naa a22 4500 510781594 CHVBK 20180411083249.0 cr unu---uuuuu 180411e20130801xx s 000 0 eng 10.1007/s11854-013-0024-z doi (NATIONALLICENCE)springer-10.1007/s11854-013-0024-z Extensions of L d -Loewner chains to higher dimensions [Elektronische Daten] [Hidetaka Hamada, Gabriela Kohr, Jerry Muir Jr.] Known results concerning the extension of normalized Loewner chains defined on the unit disk or the euclidean unit ball to higher dimensions, using either a modified Roper-Suffridge extension operator or the Pfaltzgraff-Suffridge extension operator, are shown to hold true in the more general case of L d -Loewner chains. Associated to each L d -Loewner chain on the unit ball, d ∈ [1,∞], is an evolution family and, as we show holds for the case d < ∞, a Herglotz vector field. We consider these with regard to the extended Loewner chains. To accommodate non-normalized mappings and chains, branches of extension operators are developed. As a corollary to our results, we find that these extension operators also preserve the property of starlikeness of the range of a biholomorphic mapping with respect to the point 0 lying in the closure of the range. We consider how these results can be generalized to the setting of complex Hilbert spaces and conclude with several examples. Hebrew University Magnes Press, 2013 Hamada Hidetaka Faculty of Engineering, Kyushu Sangyo University, 3-1 Matsukadai 2-Chome, 813-8503, Higashi-Ku, Fukuoka, Japan aut Kohr Gabriela Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogălniceanu Str., 400084, Cluj-Napoca, Romania aut Muir Jr. Jerry Department of Mathematics, University of Scranton, 18510, Scranton, PA, USA aut Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 120/1(2013-08-01), 357-392 0021-7670 120:1<357 2013 120 11854 https://doi.org/10.1007/s11854-013-0024-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0024-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hamada Hidetaka Faculty of Engineering, Kyushu Sangyo University, 3-1 Matsukadai 2-Chome, 813-8503, Higashi-Ku, Fukuoka, Japan aut NATIONALLICENCE 700 1- Kohr Gabriela Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogălniceanu Str., 400084, Cluj-Napoca, Romania aut NATIONALLICENCE 700 1- Muir Jr Jerry Department of Mathematics, University of Scranton, 18510, Scranton, PA, USA aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 120/1(2013-08-01), 357-392 0021-7670 120:1<357 2013 120 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer