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On Factorizations of Selfadjoint Ordinary Differential Operators
| Content Provider | Scilit |
|---|---|
| Author | Granata, Antonio |
| Copyright Year | 1982 |
| Description | Consider an ordinary linear differential operator , of order , represented by , with real-valued coefficients , , on . According to a classical result, if is formally selfadjoint on then it has a factorization of the type , where the 's are sufficiently-smooth and everywhere nonzero functions on such that . In this note we shall examine this result critically and show by means of counterexamples that the different classical proofs are either merely local or purely heuristic. A proof, which is both rigorous and global, is inferred from recent results on canonical factorizations of disconjugate operators. In addition, information is obtained on the behavior of the 's at the endpoints of which may prove useful in applications. |
| Related Links | https://www.ams.org/proc/1982-086-02/S0002-9939-1982-0667285-7/S0002-9939-1982-0667285-7.pdf |
| Ending Page | 266 |
| Page Count | 7 |
| Starting Page | 260 |
| ISSN | 00029939 |
| e-ISSN | 10886826 |
| DOI | 10.2307/2043392 |
| Journal | Proceedings of the American Mathematical Society |
| Issue Number | 2 |
| Volume Number | 86 |
| Language | English |
| Publisher | Duke University Press |
| Access Restriction | Open |
| Subject Keyword | Logic Mathematical Physics Differential Operators Selfadjoint Ordinary Differential Factorizations of Selfadjoint |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
