Abstract
We determine the form of polynomially bounded solutions to the Loewner differential equation that is satisfied by univalent subordination chains of the form f ( z , t ) = e t A z + ⋯ , where A ∈ L ( C n , C n ) has the property m ( A ) > 0 . Here m ( A ) = min { R 〈 A ( z ) , z 〉 : ‖ z ‖ = 1 } . We also give sufficient conditions for g ( z , t ) = L ( f ( z , t ) ) to be polynomially bounded, where f ( z , t ) is an A-normalized polynomially bounded Loewner chain solution to the Loewner differential equation.
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