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Abstract <p>As the Green and the Neumann functions are invariant under inversive transformations this is also true for the harmonic Robin function. This fact is proved here, implying also its conformal invariance. From the Robin function for the unit disc a respective conformal mapping gives the Robin function for the upper half plane. The Schwarz problem for analytic functions provides a direct calculation of the Robin function.</p>

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The Harmonic Robin Function for the Upper Half Plane

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • H. Begehr

摘要

Abstract

As the Green and the Neumann functions are invariant under inversive transformations this is also true for the harmonic Robin function. This fact is proved here, implying also its conformal invariance. From the Robin function for the unit disc a respective conformal mapping gives the Robin function for the upper half plane. The Schwarz problem for analytic functions provides a direct calculation of the Robin function.