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dc.contributor.authorLocker, John
dc.descriptionAugust 29, 2006.
dc.descriptionIncludes bibliographical references (pages 305-307) and index.
dc.description.abstractIn this monograph the author develops the spectral theory for an nth order two-point differential operator L in the Hilbert space L2[0,1], where L is determined by an nth order formal differential operator ℓ having variable coefficients and by n linearly independent boundary values B1,…,Bn. Using the Birkhoff approximate solutions of the differential equation (ρnI−ℓ)u=0, the differential operator L is classified as belonging to one of three possible classes: regular, simply irregular, or degenerate irregular. For the regular and simply irregular classes, the author develops asymptotic expansions of solutions of the differential equation (ρnI−ℓ)u=0, constructs the characteristic determinant and Green's function, characterizes the eigenvalues and the corresponding algebraic multiplicities and ascents, and shows that the generalized eigenfunctions of L are complete in L2[0,1]. He also gives examples of degenerate irregular differential operators illustrating some of the unusual features of this class.
dc.description.tableofcontents1. Introduction -- 2. Birkhoff approximate solutions -- 3. The approximate characteristic determinant: classification -- 4. Asymptotic expansion of solutions -- 5. The characteristic determinant -- 6. The Green's function -- 7. The eigenvalues for n even -- 8. The eigenvalues for n odd -- 9. Completeness of the generalized eigenfunctions -- 10. The case L = T, degenerate irregular examples -- 11. Unsolved problems -- 12. Appendix.
dc.format.mediumborn digital
dc.publisherColorado State University. Libraries
dc.relationCatalog record number (MMS ID): 991031654838903361
dc.relationQA193.L63 2008eb
dc.relation.hasversionLocker, John, Eigenvalues and Completeness for Regular and Simply Irregular Two-Point Differential Operators. Memoirs of the American Mathematical Society 195, no. 911. American Mathematical Society: Providence, RI (2008).
dc.relation.ispartofFaculty Publications - Department of Mathematics
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see
dc.rights.licenseThis book is open access and distributed under the terms and conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0).
dc.subject.lcshDifferential operators
dc.titleEigenvalues and completeness for regular and simply irregular two-point differential operators

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