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Remarks on spectra of operator rot. (English) Zbl 0676.47012
Spectral properties of the operator rot have been studied in various function spaces of vector fields on a three dimensional domain. A self- adjoint operator associated with rot has been introduced by choosing appropriate boundary conditions. Eigenfunctions of the self-adjoint rot operator span the orthogonal complement of the irrotational fields in the Lebesgue space \(L^ 2(\Omega)\) of square integrable vector fields. Eigenvalue problems for rot have been also discussed under different boundary conditions.
Reviewer: Z.Yoshida

MSC:
47B25 Linear symmetric and selfadjoint operators (unbounded)
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
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References:
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