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Shearing Process and an Example of a Bounded Support Function in $$S^0(\mathbb B^2)$$ S 0 ( B 2 )

Shearing Process and an Example of a Bounded Support Function in $$S^0(\mathbb B^2)$$ S 0... We introduce a process, that we call shearing, which for any given normal Loewner chain produces a normal Loewner chain made of shears automorphisms. As an application, and in stringent contrast to the one-dimensional case, we prove the existence of a starlike bounded function in the class $$S^0$$ S 0 of the ball $$\mathbb B^2$$ B 2 (in fact the restriction of a shear automorphism of $$\mathbb C^2$$ C 2 ) which is a support point for a linear continuous functional. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Shearing Process and an Example of a Bounded Support Function in $$S^0(\mathbb B^2)$$ S 0 ( B 2 )

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Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-014-0096-5
Publisher site
See Article on Publisher Site

Abstract

We introduce a process, that we call shearing, which for any given normal Loewner chain produces a normal Loewner chain made of shears automorphisms. As an application, and in stringent contrast to the one-dimensional case, we prove the existence of a starlike bounded function in the class $$S^0$$ S 0 of the ball $$\mathbb B^2$$ B 2 (in fact the restriction of a shear automorphism of $$\mathbb C^2$$ C 2 ) which is a support point for a linear continuous functional.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Nov 6, 2014

References