EIGENVALUES OF HOLOMORPHIC FUNCTIONS FOR THE THIRD BOUNDARY CONDITION

Journal article

Authors/Editors

Siginer, Dennis

Research Areas

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Publication Details

Author list: Mohammed A, Siginer DA, Akyildiz FT

Publisher: American Mathematical Society

Place: BOSTON

Publication year: 2015

Journal acronym: Q APPL MATH

Volume number: 73

Issue number: 3

Start page: 553

End page: 574

Number of pages: 22

ISSN: 0033-569X

eISSN: 1552-4485

Languages: English-Great Britain (EN-GB)

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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.

Keywords

boundary value problems, Eigenvalue, Fourier series, Fuchsian differential equations, holomorphic functions, Riemann-Hilbert-Poincare problem, the third boundary condition

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