Computational Methods and Function Theory 7 (2007), No. 2, 379--399
Copyright Heldermann Verlag 2007
John A. Pfaltzgraff
jap@math.unc.edu , University of North Carolina, Department of Mathematics, Chapel Hill, NC 27599-3250, U.S.A.
Ted J. Suffridge
ted@ms.uky.edu , University of Kentucky, Department of Mathematics, Lexington, KY 40506-0027, U.S.A.
This work is concerned with locally biholomorphic mappings on the unit ball of complex n-dimensional space. We define a concept called K-invariance and give a complete characterization of K-invariant functions. We also explore the connection between K-invariance and the solution of extremal problems in certain linear invariant families.
Keywords: Locally biholomorphic mapping, linear invariance, invariant function, extremal function.
MSC 2000: Primary 32H02; Secondary 30C45, 30C55.
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