2003/01/13 by А. А. Vladimirov, A. A. Vladimirov, Vladimirov, A. A.
Computer Science · Mathematics · #34L15 #47B25 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math.FA #msc:34L15 #msc:47B25
paper · pdf · doi:10.48550/arxiv.math/0301129
9 pages
openalex publication_date 2003/01/13 · arxiv created 2003/01/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider an operator function (F(λ)) for (λ∈(σ,τ)⊆\mathbb R) whose values are semibounded selfadjoint operators in Hilbert space (\mathfrak H). Our main goal is to estimate the number (\mathcal NF(α,β)) of the eigenvalues of (F(λ)) on a segment ([α,β)\Subset(σ,τ)). In particular, we prove the estimates (\mathcal NF(α,β)\geqslant νF(β)-νF(α)) and (\mathcal NF(α,β)= νF(β)-νF(α)) where (ν(ξ)) is the number of the negative eigenvalues of the operator (F(ξ)), (ξ∈(σ,τ)). The obtained results are applied for the functions of ordinary differential operators on a finite interval.