Eigenvalues and completeness for regular and simply irregular two-point differential operators
| dc.contributor.author | Locker, John, author | |
| dc.date.accessioned | 2015-12-09T16:27:51Z | |
| dc.date.available | 2015-12-09T16:27:51Z | |
| dc.date.issued | 2006 | |
| dc.description | August 29, 2006. | |
| dc.description.abstract | In 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.tableofcontents | 1. 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.medium | born digital | |
| dc.format.medium | books | |
| dc.identifier.uri | http://hdl.handle.net/10217/170086 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation | Catalog record number (MMS ID): 991031654838903361 | |
| dc.relation | QA193.L63 2008eb | |
| dc.relation.hasversion | Locker, 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.ispartof | Faculty Publications | |
| dc.rights.license | This 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.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.subject.lcsh | Eigenvalues | |
| dc.subject.lcsh | Differential operators | |
| dc.title | Eigenvalues and completeness for regular and simply irregular two-point differential operators | |
| dc.type | Text |
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