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Boundary Eigenvalues of Pluriharmonic Functions for the Third Boundary Condition on the Unit Polydiscs

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Analysis as a Life

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Abstract

The paper provides explicit eigenvalues and eigenfunctions of pluriharmonic functions for the third boundary condition on the unit polydiscs. It is shown that in the case of eigenvalue, for each eigenvalue, there are multiple eigenfunctions. Compatibility and solvability conditions are also studied for the case of inhomogeneous third boundary condition.

To the 80 th birthday of Heinrich Begehr

This work was completed in spring 2018 at Khalifa University.

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Authors and Affiliations

  1. Department of Mathematics, Khalifa University, Abu Dhabi, UAE

    Alip Mohammed

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  1. Alip Mohammed
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Correspondence to Alip Mohammed .

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Editors and Affiliations

  1. Department of Economics, Belarusian State University, Minsk, Belarus

    Sergei Rogosin

  2. Mathematics Department, Yeditepe University, AtaĹźehir, Istanbul, Turkey

    Ahmet Okay Çelebi

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Mohammed, A. (2019). Boundary Eigenvalues of Pluriharmonic Functions for the Third Boundary Condition on the Unit Polydiscs. In: Rogosin, S., Çelebi, A. (eds) Analysis as a Life. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-02650-9_3

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