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Complex Analysis and Operator Theory

, Volume 11, Issue 4, pp 895–926 | Cite as

Finding Eigenvalues and Eigenfunctions of the Zaremba Problem for the Circle

  • Ari Laptev
  • Anastasiya PeichevaEmail author
  • Alexander Shlapunov
Article

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.

Keywords

Sturm-Liouville problems Robin condition Eigenvalues 

Mathematics Subject Classification

47A10 35J57 30B60 

Notes

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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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Imperial College LondonLondonUK
  2. 2.Institute of Mathematics and Computer ScienceSiberian Federal UniversityKrasnoyarskRussia

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