Spectrum of a non-self-adjoint operator associated with the periodic heat equation
- Chugunova, Marina
- Pelinovsky, Dmitry
Publication date
June 2008
DOI Publisher
Elsevier Inc. ISSN
0022-247X Citation count (estimate)
18Abstract
AbstractWe study the spectrum of the linear operator L=−∂θ−ϵ∂θ(sinθ∂θ) subject to the periodic boundary conditions on θ∈[−π,π]. We prove that the operator is closed in Lper2([−π,π]) with the domain in Hper1([−π,π]) for |ϵ|<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 Lper2([−π,π])
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