Spectrum of a non-self-adjoint operator associated with the periodic heat equation |
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Authors: | Marina Chugunova |
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Institution: | Department of Mathematics, McMaster University, Hamilton, Ontario, Canada, L8S 4K1 |
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Abstract: | We study the spectrum of the linear operator L=−θ∂−?θ∂(sinθθ∂) subject to the periodic boundary conditions on θ∈−π,π]. We prove that the operator is closed in with the domain in for |?|<2, its spectrum consists of an infinite sequence of isolated eigenvalues and the set of corresponding eigenfunctions is complete. By using numerical approximations of eigenvalues and eigenfunctions, we show that all eigenvalues are simple, located on the imaginary axis and the angle between two subsequent eigenfunctions tends to zero for larger eigenvalues. As a result, the complete set of linearly independent eigenfunctions does not form a basis in . |
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Keywords: | Spectrum of a non-self-adjoint operator Advection-diffusion equation with periodic coefficients Completeness and basis of eigenfunctions Numerical approximation of eigenvalues and eigenfunctions |
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