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Finding eigenvalues and eigenfunctions of the Zaremba problem for the circle. (English) Zbl 1367.47052

Summary: 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.

MSC:

47F05 General theory of partial differential operators
35J57 Boundary value problems for second-order elliptic systems
30B60 Completeness problems, closure of a system of functions of one complex variable
34B24 Sturm-Liouville theory
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