Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Julia theory for slice regular functions
HTML articles powered by AMS MathViewer

by Guangbin Ren and Xieping Wang PDF
Trans. Amer. Math. Soc. 369 (2017), 861-885 Request permission

Abstract:

Slice regular functions have been extensively studied over the past decade, but much less is known about their boundary behavior. In this paper, we initiate the study of Julia theory for slice regular functions. More specifically, we establish the quaternionic versions of the Julia lemma, the Julia-Carathéodory theorem, the boundary Schwarz lemma, and the Burns-Krantz rigidity theorem for slice regular self-mappings of the open unit ball $\mathbb {B}$ and of the right half-space $\mathbb {H}^+$. Our quaternionic boundary Schwarz lemma involves a Lie bracket reflecting the non-commutativity of quaternions. Together with some explicit examples, it shows that the slice derivative of a slice regular self-mapping of $\mathbb {B}$ at a boundary fixed point is not necessarily a positive real number, in contrast to that in the complex case, meaning that its commonly believed version turns out to be totally wrong.
References
Similar Articles
Additional Information
  • Guangbin Ren
  • Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei 230026, People’s Republic of China
  • Email: rengb@ustc.edu.cn
  • Xieping Wang
  • Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei 230026, People’s Republic of China
  • MR Author ID: 1110977
  • Email: pwx@mail.ustc.edu.cn
  • Received by editor(s): January 28, 2015
  • Published electronically: March 18, 2016
  • Additional Notes: This work was supported by the NNSF of China (11371337), RFDP (20123402110068).
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 861-885
  • MSC (2010): Primary 30G35, 30C80, 32A40, 31B25
  • DOI: https://doi.org/10.1090/tran/6717
  • MathSciNet review: 3572257