Energy-Critical NLS with Quadratic Potentials

DOI10.1080/03605300903328109zbMath1188.33015arXivmath/0611394OpenAlexW2045071910MaRDI QIDQ3653283

Monica Visan, Xiaoyi Zhang, Rowan Killip

Publication date: 22 December 2009

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611394

zbMATH Keywords

orthogonal polynomialsJacobi matricesspectral theoryrandom perturbationsratio asymptoticsVerblunsky coefficientsreflectionless operatorsweak asymptotic convergenceright limitsRemling's theoremCanter-Moral-Vélazquez (CMV) matricesreflectionless probability measures

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Hermitian, skew-Hermitian, and related matrices (15B57) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (12)

Energy-critical Hartree equation with harmonic potential for radial data ⋮ Energy-critical NLS with potentials of quadratic growth ⋮ On ground states for the 2D Schrödinger equation with combined nonlinearities and harmonic potential ⋮ Filtering the \(L^2\)-critical focusing Schrödinger equation ⋮ Blow-up criteria below scaling for defocusing energy-supercritical NLS and quantitative global scattering bounds ⋮ Threshold for blowup and stability for nonlinear Schrödinger equation with rotation ⋮ Scattering theory for nonlinear Schrödinger equations with inverse-square potential ⋮ The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions ⋮ Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data ⋮ Global Well-Posedness for Cubic NLS with Nonlinear Damping ⋮ The energy-critical quantum harmonic oscillator ⋮ Asymptotic Behavior of the Nonlinear Schrödinger Equation with Harmonic Trapping

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