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The Riesz base of a spectral problem with infinitely multiple eigen- values. (Russian. English summary) Zbl 0583.47025
Such a non-self-adjoint problem for the Laplace operator in a rectangle \({\mathcal D}\) is constructed that each number of a given countable subset in the reals is an eigenvalue with infinite multiplicity. To any of such eigenvalues there correspond infinitely many eigenfunctions as well as adjoint functions. However, the set of all eigenfunctions and of all adjoint functions for this problem forms a Riesz basis in \(L_ 2{\mathcal D}\).
MSC:
47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
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