Asymptotics of the spectral data of perturbed Stark operators in the half-line with mixed boundary conditions

2025/05/21 by Julio H. Toloza, Toloza, Julio H., Alfredo Uribe +1
Mathematics · #34E10 #34L15 #81Q05 #81Q10 #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2505.15943

openalex publication_date 2025/05/21 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

We obtain sharp asymptotic formulas for the eigenvalues and norming constants of Sturm-Liouville operators associated with the differential expression -(d²)/(dx²) + x + q(x), x∈ [0,∞), together with the boundary condition φ'(0) - bφ(0) =0, b∈ℝ, where q∈ \ p∈ L²_ℝ(ℝ₊,(1+x)^r dx) : p'∈ L²_ℝ(ℝ₊,(1+x)^r dx)\ with r>1.

Citations

• The Dirichlet problem for perturbed Stark operators in the half-line
• The inverse problem for perturbed harmonic oscillator on the half-line

Related

• One-dimensional Stark operators in the half-line
• The Dirichlet problem for perturbed Stark operators in the half-line
• Asymptotic formulae for eigenvalues and eigenfunctions of Sturm--Liouville operators with potentials---distributions. Dirichlet--Neumann boundary conditions
• The inverse Sturm-Liouville problem with mixed boundary conditions
• On a class of spectral problems on the half-line and their applications to multi-dimensional problems