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Finding Eigenvalues and Eigenfunctions of the Zaremba Problem for the Circle

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Abstract

We consider Zaremba type boundary value problem for the Laplace operator in the unit circle on the complex plane. Using the theorem on the exponential representation for solutions to equations with constant coefficients we indicate a way to find eigenvalues of the problem and to construct its eigenfunctions.

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Acknowledgments

The work was supported by the grant of the Russian Federation Government for scientific research under the supervision of leading scientist at the Siberian Federal University, contract N. 14.Y26.31.0006, and by RFBR Grant 14-01-00544.

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Correspondence to Anastasiya Peicheva.

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Communicated by Terhorst, Dr. Dmitry, Dr. Izchak and Prof. Alpay.

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Laptev, A., Peicheva, A. & Shlapunov, A. Finding Eigenvalues and Eigenfunctions of the Zaremba Problem for the Circle. Complex Anal. Oper. Theory 11, 895–926 (2017). https://doi.org/10.1007/s11785-016-0603-y

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  • DOI: https://doi.org/10.1007/s11785-016-0603-y

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