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

Abstract

We obtain sharp asymptotic formulas for the eigenvalues and norming constants of Sturm-Liouville operators associated with the differential expression \[ -\frac{d^2}{dx^2} + x + q(x), \quad x\in [0,\infty), \] together with the boundary condition ${\phi }^{\prime }(0)-b\phi (0)=0$, $b\in \mathbb{R}$, where \[ q\in \left\{ p\in L^2_{\mathbb{R}}(\mathbb{R}_+,(1+x)^r dx) : p'\in L^2_{\mathbb{R}}(\mathbb{R}_+,(1+x)^r dx)\right\} \] with $r>1$.

32 pages, no figures, some typographical errors corrected