g-Loewner chains, Bloch functions and extension operators into the family of locally biholomorphic mappings in infinite dimensional spaces

Authors

  • Ian GRAHAM Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada, e-mail: graham@math.toronto.edu https://orcid.org/0000-0002-2278-2686
  • Hidetaka HAMADA Faculty of Science and Engineering, Kyushu Sangyo University, 3-1 Matsukadai 2-Chome, Higashi-ku Fukuoka 813-8503, Japan, e-mail: h.hamada@ip.kyusan-u.ac.jp https://orcid.org/0000-0003-1151-2100
  • †Gabriela KOHR Faculty of Mathematics and Computer Science, Babe¸s-Bolyai University, 1 M. Kog˘alniceanu Str., 400084 Cluj-Napoca, Romania, e-mail: gkohr@math.ubbcluj.ro
  • Mirela KOHR Faculty of Mathematics and Computer Science, Babe¸s-Bolyai University, 1 M. Kog˘alniceanu Str., 400084 Cluj-Napoca, Romania, e-mail: mkohr@math.ubbcluj.ro

DOI:

https://doi.org/10.24193/subbmath.2022.2.01

Keywords:

Bloch function, complex Banach space, Loewner chain, Muir type extension operator, Roper-Suffridge type extension operator, Pfaltzgraff-Suffridge type extension operator.

Abstract

In this paper, we survey recent results obtained by the authors on the preservations of the first elements of (g-) Loewner chains and the Bloch mappings by the Roper-Suffridge type extension operators, the Muir type extension opera- tors and the Pfaltzgraff-Suffridge type extension operators into the mappings on the domains in the complex Banach spaces.

Mathematics Subject Classification (2010): 32A18, 32A30, 32K05, 30C45, 30C80, 30D45.

Received 20 January 2022; Accepted 27 January 2022.

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STUDIA UBB MATHEMATICA, Volume 67 (LXVII), No. 2, June 2022

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2022-06-10

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GRAHAM, I., HAMADA, H., KOHR, †Gabriela, & KOHR, M. (2022). g-Loewner chains, Bloch functions and extension operators into the family of locally biholomorphic mappings in infinite dimensional spaces. Studia Universitatis Babeș-Bolyai Mathematica, 67(2), 219–236. https://doi.org/10.24193/subbmath.2022.2.01

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Volume 67, No. 2, June 2022

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