The estimates for the number of the eigenvalues of abstract and differential operator functions
| dc.creator | Vladimirov, A. A. | |
| dc.date | 2003-01-13 | |
| dc.date | 2003-01-16 | |
| dc.date.accessioned | 2026-07-07T04:54:25Z | |
| dc.date.available | 2026-07-07T04:54:25Z | |
| dc.description | We consider an operator function (F(λ)) for (λ\in(σ,τ)\subseteq\mathbb R) whose values are semibounded selfadjoint operators in Hilbert space (\mathfrak H). Our main goal is to estimate the number (\mathcal N_F(α,β)) of the eigenvalues of (F(λ)) on a segment ([α,β)\Subset(σ,τ)). In particular, we prove the estimates (\mathcal N_F(α,β)\geqslant ν_F(β)-ν_F(α)) and (\mathcal N_F(α,β)= ν_F(β)-ν_F(α)) where (ν(ξ)) is the number of the negative eigenvalues of the operator (F(ξ)), (ξ\in(σ,τ)). The obtained results are applied for the functions of ordinary differential operators on a finite interval. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0301129 | |
| dc.identifier | http://arxiv.org/abs/math/0301129 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66245 | |
| dc.subject | Functional Analysis | |
| dc.subject | 47B25; 34L15 | |
| dc.title | The estimates for the number of the eigenvalues of abstract and differential operator functions | |
| dc.type | text |