On Spectral Properties of Schrödinger-Type Operator with Complex Potential

1996 ◽  
pp. 164-176 ◽  
Author(s):  
Edward Grinshpun
Keyword(s):  
Complex Potential ◽  
Spectral Properties ◽  
Type Operator ◽  
Schrödinger Type Operator

On the spectrum and the distribution of singular values of Schrödinger operators with a complex potential

1983 ◽  
Vol 388 (1794) ◽  
pp. 195-218 ◽  
Keyword(s):  
Complex Potential ◽  
Spectral Properties ◽  
Polynomial Growth ◽  
Schrödinger Operators ◽  
Singular Values ◽  
Negative Real Part ◽  
Adjoint Problem ◽  
Schrodinger Operators ◽  
Asymptotic Estimates ◽  
Integrability Conditions

This paper is concerned with spectral properties of the Schrödinger operator ─ ∆+ q with a complex potential q which has non-negative real part and satisfies weak integrability conditions. The problem is dealt with as a genuine non-self-adjoint problem, not as a perturbation of a self-adjoint one, and global and asymptotic estimates are obtained for the corresponding singular values. From these estimates information is obtained about the eigenvalues of the problem. By way of illustration, detailed calculations are given for an example in which the potential has at most polynomial growth.

scholarly journals Mathematical and numerical framework for metasurfaces using thin layers of periodically distributed plasmonic nanoparticles

2016 ◽  
Vol 472 (2193) ◽  
pp. 20160445 ◽  
Author(s):  
Habib Ammari ◽  
Matias Ruiz ◽  
Wei Wu ◽  
Sanghyeon Yu ◽  
Hai Zhang
Keyword(s):  
Boundary Condition ◽  
Spectral Properties ◽  
Thin Layers ◽  
Optical Scattering ◽  
Plasmonic Nanoparticles ◽  
Type Operator ◽  
Impedance Boundary Condition ◽  
Resonant Frequencies ◽  
Impedance Boundary ◽  
Conducting Plate

In this paper, we derive an impedance boundary condition to approximate the optical scattering effect of an array of plasmonic nanoparticles mounted on a perfectly conducting plate. We show that at some resonant frequencies the impedance blows up, allowing for a significant reduction of the scattering from the plate. Using the spectral properties of a Neumann–Poincaré type operator, we investigate the dependency of the impedance with respect to changes in the nanoparticle geometry and configuration.

On the Completeness of the System of Normalized Eigenfunctions of a Nonlinear Schrödinger-Type Operator on a Segment

1997 ◽  
Vol 12 (01) ◽  
pp. 295-298 ◽  
Author(s):  
P. E. Zhidkov
Keyword(s):  
Type Operator ◽  
Nonlinear Schrödinger ◽  
Schrödinger Type Operator

In this note, a recent rigorous author's result on the completeness in the space L2 of the system of eigenfunctions of a nonlinear Schrödinger-type operator is established (without proof).

scholarly journals Fourth-order Schrödinger type operator with singular potentials

2016 ◽  
Vol 107 (3) ◽  
pp. 285-294 ◽  
Author(s):  
Federica Gregorio ◽  
Sebastian Mildner
Keyword(s):  
Fourth Order ◽  
Type Operator ◽  
Singular Potentials ◽  
Schrödinger Type Operator

scholarly journals Generic Simplicity of a Schrödinger-type Operator on the Torus

2017 ◽  
Vol 2 (1) ◽  
pp. 1-19
Author(s):  
Louis Omenyi ◽  
Emmanuel Nwaeze ◽  
McSylvester Omaba
Keyword(s):  
Type Operator ◽  
Schrödinger Type Operator

scholarly journals Wavelets, Sobolev Multipliers, and Application to Schrödinger Type Operators with Nonsmooth Potentials

2013 ◽  
Vol 2013 ◽  
pp. 1-22
Author(s):  
Pengtao Li ◽  
Qixiang Yang ◽  
Yueping Zhu
Keyword(s):  
Morrey Spaces ◽  
Type Operator ◽  
Inclusion Relation ◽  
Multiplier Space ◽  
Schrödinger Type Operator ◽  
Meyer Wavelets ◽  
Schrödinger Type Operators

We employ Meyer wavelets to characterize multiplier spaceXr,pt(ℝn)without using capacity. Further, we introduce logarithmic Morrey spacesMr,pt,τ(ℝn)to establish the inclusion relation between Morrey spaces and multiplier spaces. By fractal skills, we construct a counterexample to show that the scope of the indexτofMr,pt,τ(ℝn)is sharp. As an application, we consider a Schrödinger type operator with potentials inMr,pt,τ(ℝn).

scholarly journals p-Adic Schrödinger-type operator with point interactions

2008 ◽  
Vol 338 (2) ◽  
pp. 1267-1281 ◽  
Author(s):  
S. Albeverio ◽  
S. Kuzhel ◽  
S. Torba
Keyword(s):  
Type Operator ◽  
Point Interactions ◽  
Schrödinger Type Operator

scholarly journals Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Yu Liu ◽  
Youzheng Ding
Keyword(s):  
Weak Type ◽  
Type Operator ◽  
Reverse Hölder Class ◽  
Hölder Class ◽  
Weak Type Estimates ◽  
Holder Class ◽  
Schrödinger Type Operator ◽  
Schrödinger Type Operators ◽  
Reverse Hölder

We consider the Schrödinger-type operatorH=(−Δ)2+V2, where the nonnegative potentialVbelongs to the reverse Hölder classBq1forq1≥n/2,  n≥5. TheLpestimates of the operator∇4H−1related toHare obtained whenV∈Bq1and1<p≤q1/2. We also obtain the weak-type estimates of the operator∇4H−1under the same condition ofV.

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