Typically Real Harmonic Functions
Michael Dorff, Maria Nowak, and Wojciech Szapiel
TL;DR
This paper studies a class of harmonic functions that are typically real on the unit disk, extending known classes and exploring their univalence properties.
Contribution
It introduces the class of typically real harmonic functions and provides partial results on their univalence region.
Findings
The class contains normalized analytic and typically real functions.
Partial characterization of the univalence region for .
Extension of known classes of functions to harmonic case.
Abstract
We consider a class of typically real harmonic functions on the unit disk that contains the class of normalized analytic and typically real functions. We also obtain some partial results about the region of univalence for this class.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Differential Equations and Boundary Problems