Weighted Estimates for Bilinear Operators by Hua Zhu, Heping Liu

“…We also investigate weighted estimates for bilinear operators related to Schrödinger operator.…”
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A theorem on localized self-adjointness of Shrödinger operators with LLOC1-potentials by Hans L. Cycon

“…We prove a result which concludes the self-adjointness of a Schrödinger operator from the self-adjointness of the associated localized Schrödinger operators having LLOC1-Potentials.…”
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Eigenvalue Asymptotics of the Even-Dimensional Exterior Landau-Neumann Hamiltonian by Mikael Persson

“…We study the Schrödinger operator with a constant magnetic field in the exterior of a compact domain in ℝ2𝑑, 𝑑≥1. …”
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Nontrivial Solutions for 4-Superlinear Schrödinger–Kirchhoff Equations with Indefinite Potentials by Wei Chen, Yue Wu

“…The potential V here is indefinite so that the Schrödinger operator −Δ+V possesses a finite-dimensional negative space. …”
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Fractional powers of hyponormal operators of Putnam type by Toka Diagana

“…As an application, a large class of the Schrödinger's operator with a complex potential Q∈Lloc1(ℝd)+L∞(ℝd) is considered.…”
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A Formula for Eigenvalues of Jacobi Matrices with a Reflection Symmetry by S. B. Rutkevich

“…We obtain such requirements in the simplest case of the discrete Schrödinger operator acting in l2(N), which does not have bound and semibound states and whose potential has a compact support.…”
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Discretized representations of harmonic variables by bilateral Jacobi operators by Andreas Ruffing

“…Starting from a discrete Heisenberg algebra we solve several representation problems for a discretized quantum oscillator in a weighted sequence space. The Schrödinger operator for a discrete harmonic oscillator is derived. …”
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Boundedness of Lusin-area and gλ* functions on localized Morrey-Campanato spaces over doubling metric measure spaces by Haibo Lin, Eiichi Nakai, Dachun Yang

“…If χ has the volume regularity Property (P), the authors then establish the boundedness of the Lusin-area function, which is defined via kernels modeled on the semigroup generated by the Schrödinger operator, from ερa,p(χ) to ε̃ρa,p(χ) without invoking any regularity of considered kernels. …”
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On uniform controllability of 1D transport equations in the vanishing viscosity limit by Laurent, Camille, Léautaud, Matthieu

“…The upper/lower estimates we obtain depend on geometric quantities such as an Agmon distance and the spectral gap of an associated semiclassical Schrödinger operator. They improve, in this particular situation, the results obtained in the companion paper [38].The proofs rely on a reformulation of the problem as a uniform observability question for the semiclassical heat equation together with a fine analysis of localization of eigenfunctions both in the semiclassically allowed and forbidden regions [40], together with estimates on the spectral gap [33, 1]. …”
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Finite propagation speed and kernels of strictly elliptic operators by David Gurarie

“…The class of operators considered in the paper is of the form A0+B with the leading elliptic part A0 and a singular perturbation B, whose coefficients have Lp-type and are modeled after Schrödinger operators.…”
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Harmonic analysis on the quantized Riemann sphere by Jaak Peetre, Genkai Zhang

“…It turns out that the eigenvalue problem of the corresponding invariant Laplacean is equivalent to an infinite system of one dimensional Schrödinger operators. They correspond to the Morse potential in the case of the disk. …”
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