Shearing Process and an Example of a Bounded Support Function in
F Bracci - Computational Methods and Function Theory, 2015 - Springer
Computational Methods and Function Theory, 2015•Springer
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.
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.
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 of the ball (in fact the restriction of a shear automorphism of ) which is a support point for a linear continuous functional.
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