Generalised Dirac-Schrödinger operators and the Callias Theorem by Koen van den Dungen

“…We consider generalised Dirac-Schrödinger operators, consisting of a self-adjoint elliptic first-order differential operator $\mathcal {D}$ with a skew-adjoint ‘potential’ given by a (suitable) family of unbounded operators. …”
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Internal Lifshitz tails for discrete Schrödinger operators by Hatem Najar

“…We consider random Schrödinger operators Hω acting on l2(ℤd). We adapt the technique of the periodic approximations used in (2003) for the present model to prove that the integrated density of states of Hω has a Lifshitz behavior at the edges of internal spectral gaps if and only if the integrated density of states of a well-chosen periodic operator is nondegenerate at the same edges. …”
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On the boundary part spectrum of the discrete Schrödinger operator by Arvydas Astrauskas

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On the Singular Spectrum for Adiabatic Quasiperiodic Schrödinger Operators by Magali Marx, Hatem Najar

“…We study spectral properties of a family of quasiperiodic Schrödinger operators on the real line in the adiabatic limit. …”
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Hardy Spaces Associated to Schrödinger Operators on Product Spaces by Liang Song, Chaoqiang Tan

“…Let L=−Δ+V be a Schrödinger operator on ℝn, where V∈Lloc1(ℝn) is a nonnegative function on ℝn. …”
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Ground State for the Schrödinger Operator with the Weighted Hardy Potential by J. Chabrowski, K. Tintarev

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The Boundedness of Marcinkiewicz Integrals Associated with Schrödinger Operator on Morrey Spaces by Dongxiang Chen, Fangting Jin

“…Let L=-Δ+V be a Schrödinger operator, where V belongs to some reverse Hölder class. …”
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The Boundedness of Marcinkiewicz Integral Associated with Schrödinger Operator and Its Commutator by Dongxiang Chen, Dan Zou

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Commutators of Higher Order Riesz Transform Associated with Schrödinger Operators by Yu Liu, Lijuan Wang, Jianfeng Dong

“…Let L=-Δ+V be a Schrödinger operator on ℝn (n≥3), where V≢0 is a nonnegative potential belonging to certain reverse Hölder class Bs for s≥n/2. …”
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Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator by Abd-Allah Hyder, M. EL-Badawy

“…In this paper, we investigate the distributed optimal control problem for time-fractional differential system involving Schrödinger operator defined on Rn. The time-fractional derivative is considered in the Riemann-Liouville sense. …”
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Signal denoising based on the Schrödinger operator's eigenspectrum and a curvature constraint by P. Li, T.M. Laleg‐Kirati

“…Abstract The authors propose an adaptive, general and data‐driven curvature penalty for signal denoising via the Schrödinge operator. The term is derived by assuming noise to be generally Gaussian distributed, a widely applied assumption in most 1D signal denoising applications. …”
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Existence of solutions for non-necessarily cooperative systems involving Schrödinger operators by Laure Cardoulis

“…We study the existence of a solution for a non-necessarily cooperative system of n equations involving Schrödinger operators defined on ℝN and we study also a limit case (the Fredholm Alternative (FA)). …”
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The Boundedness of Some Integral Operators on Weighted Hardy Spaces Associated with Schrödinger Operators by Hua Wang

“…Let L=-Δ+V be a Schrödinger operator acting on L2(Rn), n≥1, where V≢0 is a nonnegative locally integrable function on Rn. …”
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The boundedness of commutator of Riesz transform associated with Schrödinger operators on a Hardy space by Canqin Tang, Chuanmei Bi

“…In this paper, we study the boundedness of commutator [b,T] of Riesz transform associated with Schrödinger operator and b is BMO type function, note that the kernel of T has no smoothness, and the boundedness from Hb1(Rn)→L1(Rn) is obtained.…”
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Weighted Morrey Spaces Related to Schrödinger Operators with Nonnegative Potentials and Fractional Integrals by Hua Wang

“…Let ℒ=−Δ+V be a Schrödinger operator on ℝd, d≥3, where Δ is the Laplacian operator on ℝd, and the nonnegative potential V belongs to the reverse Hölder class RHs with s≥d/2. …”
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The Higher Order Riesz Transform and BMO Type Space Associated with Schrödinger Operators on Stratified Lie Groups by Yu Liu, Jianfeng Dong

“…Let L=-Δ+W be a Schrödinger operator on the stratified Lie group G. In this paper, we prove the boundedness of some integral operators related to L, such as L-1∇2, L-1W, and L-1(-Δ) on the space BMOL(G).…”
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Quantitative Weighted Bounds for Littlewood-Paley Functions Generated by Fractional Heat Semigroups Related with Schrödinger Operators by Li Yang, Pengtao Li

“…Let L=−Δ+V be a Schrödinger operator on ℝn, where Δ denotes the Laplace operator ∑i=1n∂2/∂xi2 and V is a nonnegative potential belonging to a certain reverse Hölder class RHqℝn with q>n/2. …”
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Eigenvalues asymptotics for Stark operators by Hatem Najar, Monia Raissi

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A Nonlinear Schrödinger Equation Resonating at an Essential Spectrum by Shaowei Chen, Haijun Zhou

“…The potential function V satisfies that the essential spectrum of the Schrödinger operator -Δ-V is [0,+∞) and this Schrödinger operator has infinitely many negative eigenvalues accumulating at zero. …”
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An application to Kato's square root problem by Toka Diagana

“…We find all complex potentials Q such that the general Schrödinger operator on ℝn, given by L=−Δ+Q, where Δ is the Laplace differential operator, verifies the well-known Kato's square problem. …”
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