Eigenvalues of holomorphic functions for the third boundary condition

Mohammed, Alip; Siginer, Dennis; Akyildiz, Fahir

doi:10.1090/qam/1419

Authors: Alip Mohammed, Dennis A. Siginer and Fahir Talay Akyildiz
Journal: Quart. Appl. Math. 73 (2015), 553-574
MSC (2010): Primary 30E25, 35J35, 35J45
DOI: https://doi.org/10.1090/qam/1419
Published electronically: June 16, 2015
MathSciNet review: 3400759
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Abstract: The eigenvalue problem of holomorphic functions on the unit disc for the third boundary condition with general coefficient is studied using Fourier analysis. With a general anti-polynomial coefficient a variable number of additional boundary conditions need to be imposed to determine the eigenvalue uniquely. An additional boundary condition is required to obtain a unique eigenvalue when the coefficient includes an essential singularity rather than a pole. In either case explicit solutions are derived.

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