Continuous spectrum and square-integrable solutions of differential operators with intermediate deficiency index

DOI10.1016/j.jfa.2008.08.007zbMath1165.34052OpenAlexW2074490432MaRDI QIDQ960545

Aiping Wang, Anton Zettl, Jiong Sun

Publication date: 22 December 2008

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2008.08.007

zbMATH Keywords

continuous spectrumdifferential operatorssingular boundary conditionsintermediate deficiency indicessquare-integrable solutions

Mathematics Subject Classification ID

General spectral theory of ordinary differential operators (34L05) General theory of ordinary differential operators (47E05)

Related Items (17)

Dissipative operators, symplectic geometry, and limit-circle solutions ⋮ Spectral properties of singular discrete linear Hamiltonian systems ⋮ Characterization of domains of self-adjoint ordinary differential operators. II ⋮ Classification of self-adjoint domains of odd-order differential operators with matrix theory ⋮ Real-parameter square-integrable solutions and the spectrum of differential operators ⋮ Characterization of self-adjoint domains for differential operators with interior singular points ⋮ Symmetric operators with real defect subspaces of the maximal dimension. Applications to differential operators ⋮ Spectra of a class of non-symmetric operators in Hilbert spaces with applications to singular differential operators ⋮ On essential spectra of singular linear Hamiltonian systems ⋮ The spectrum of differential operators and square-integrable solutions ⋮ Survey article: Self-adjoint ordinary differential operators and their spectrum ⋮ Relatively bounded and relatively compact perturbations for limit circle Hamiltonian systems ⋮ Eigenvalues of limit-point Sturm-Liouville problems ⋮ Simplicity and spectrum of singular Hamiltonian systems of arbitrary order ⋮ Essential spectrum of singular discrete linear Hamiltonian systems ⋮ Self-adjoint extensions for linear Hamiltonian systems with two singular endpoints ⋮ \(\mathcal{J}\)-self-adjoint extensions of a class of Hamiltonian differential systems

Cites Work

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• Characterization of domains of self-adjoint ordinary differential operators
• Spectral theory of ordinary differential operators
• Formally self-adjoint quasidifferential operators
• The deficiency index problem for powers of ordinary differential expressions
• Symmetric differential operators and their Friedrichs extensions
• Floquet theory for left-definite Sturm-Liouville problems
• Introduction to spectral theory. With applications to Schrödinger operators
• Complex symplectic geometry with applications to ordinary differential operators
• Equivalence, adjoints and symmetry of quasi-differential expressions with matrix-valued coefficients and polynomials in them
• An Oscillation Theorem for Continuous Spectra
• A Separation Theorem for Continuous Spectra

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