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dc.contributor.authorLocker, John
dc.date.accessioned2015-12-09T16:27:51Z
dc.date.available2015-12-09T16:27:51Z
dc.date.issued2006
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.format.mediumbooks
dc.identifier.urihttp://hdl.handle.net/10217/170086
dc.languageEnglish
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). http://dx.doi.org/10.1090/memo/0911
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 https://libguides.colostate.edu/copyright.
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.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subject.lcshEigenvalues
dc.subject.lcshDifferential operators
dc.titleEigenvalues and completeness for regular and simply irregular two-point differential operators
dc.typeText


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