Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Eigenvalues of holomorphic functions for the third boundary condition


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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Additional Information

Alip Mohammed
Affiliation: Department of Mathematics, Arts and Sciences, The Petroleum Institute, Abu Dhabi, United Arab Emirates
Email: aalifu@pi.ac.ae

Dennis A. Siginer
Affiliation: Department of Mechanical Engineering and Department of Applied Mathematics, Botswana International University of Science and Technology Palapye, Botswana; Centro de Investigación en Creatividad y Educación Superior, Universidad de Santiago de Chile, Santiago, Chile
Email: siginerd@biust.ac.bw, dennis.siginer@usach.cl

Fahir Talay Akyildiz
Affiliation: Department of Mathematics, College of Arts and Sciences, Gaziantep University, Gaziantep, Turkey
Email: fakyildiz@gantep.edu.tr

DOI: https://doi.org/10.1090/qam/1419
Keywords: Eigenvalue, boundary value problems, Riemann-Hilbert-Poincar\'e problem, the third boundary condition, holomorphic functions, Fourier series, Fuchsian differential equations
Received by editor(s): December 4, 2013
Received by editor(s) in revised form: September 29, 2014
Published electronically: June 16, 2015
Article copyright: © Copyright 2015 Brown University


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