American Institute of Mathematical Sciences

Advanced
September  2010, 14(2): 559-586. doi: 10.3934/dcdsb.2010.14.559

Remarks on a paper of Kotani concerning generalized reflectionless Schrödinger potentials

Russell Johnson 1, and  Luca Zampogni 2,

1. 

Dipartimento di Sistemi e Informatica, Università di Firenze, Via di S. Marta 3, 50139 Firenze
2. 

Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy

Received  September 2009 Revised  December 2009 Published  June 2010

The class of generalized reflectionless Schrödinger potentials was introduced by Marchenko-Lundina and was analyzed by Kotani. We state and prove various results concerning those stationary ergodic processes of Schrödinger potentials which are contained in this class.
Keywords: stationary ergodic processes., Sato-Segal-Wilson potentials, Generalized reflectionless potentials.
Mathematics Subject Classification: Primary: 37B55, 47B80; Secondary: 34A55, 34L4.
Citation: Russell Johnson, Luca Zampogni. Remarks on a paper of Kotani concerning generalized reflectionless Schrödinger potentials. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 559-586. doi: 10.3934/dcdsb.2010.14.559
[1]

Russell Johnson, Luca Zampogni. Some examples of generalized reflectionless Schrödinger potentials. Discrete & Continuous Dynamical Systems - S, 2016, 9 (4) : 1149-1170. doi: 10.3934/dcdss.2016046
[2]

Martin Heida, Alexander Mielke. Averaging of time-periodic dissipation potentials in rate-independent processes. Discrete & Continuous Dynamical Systems - S, 2017, 10 (6) : 1303-1327. doi: 10.3934/dcdss.2017070
[3]

Alessandro Selvitella. Qualitative properties of stationary solutions of the NLS on the Hyperbolic space without and with external potentials. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2663-2677. doi: 10.3934/cpaa.2019118
[4]

Jorge Tejero. Reconstruction of rough potentials in the plane. Inverse Problems & Imaging, 2019, 13 (4) : 863-878. doi: 10.3934/ipi.2019039
[5]

Vagif S. Guliyev, Ramin V. Guliyev, Mehriban N. Omarova, Maria Alessandra Ragusa. Schrödinger type operators on local generalized Morrey spaces related to certain nonnegative potentials. Discrete & Continuous Dynamical Systems - B, 2020, 25 (2) : 671-690. doi: 10.3934/dcdsb.2019260
[6]

J. Douglas Wright. On the spectrum of the superposition of separated potentials.. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 273-281. doi: 10.3934/dcdsb.2013.18.273
[7]

Huan-Zhen Chen, Zhongxue Lü. Positive solutions to involving Wolff potentials. Communications on Pure & Applied Analysis, 2014, 13 (2) : 773-788. doi: 10.3934/cpaa.2014.13.773
[8]

Erik Lindgren, Peter Lindqvist. Infinity-harmonic potentials and their streamlines. Discrete & Continuous Dynamical Systems, 2019, 39 (8) : 4731-4746. doi: 10.3934/dcds.2019192
[9]

Ruikuan Liu, Tian Ma, Shouhong Wang, Jiayan Yang. Thermodynamical potentials of classical and quantum systems. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1411-1448. doi: 10.3934/dcdsb.2018214
[10]

Paulo Cesar Carrião, R. Demarque, Olímpio H. Miyagaki. Nonlinear Biharmonic Problems with Singular Potentials. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2141-2154. doi: 10.3934/cpaa.2014.13.2141
[11]

Bastian Gebauer. Localized potentials in electrical impedance tomography. Inverse Problems & Imaging, 2008, 2 (2) : 251-269. doi: 10.3934/ipi.2008.2.251
[12]

Guy Cohen, Jean-Pierre Conze. The CLT for rotated ergodic sums and related processes. Discrete & Continuous Dynamical Systems, 2013, 33 (9) : 3981-4002. doi: 10.3934/dcds.2013.33.3981
[13]

Jun Wang, Lu Xiao. Existence and concentration of solutions for a Kirchhoff type problem with potentials. Discrete & Continuous Dynamical Systems, 2016, 36 (12) : 7137-7168. doi: 10.3934/dcds.2016111
[14]

Marc Rauch. Variational principles for the topological pressure of measurable potentials. Discrete & Continuous Dynamical Systems - S, 2017, 10 (2) : 367-394. doi: 10.3934/dcdss.2017018
[15]

Nicolas Fournier. A new regularization possibility for the Boltzmann equation with soft potentials. Kinetic & Related Models, 2008, 1 (3) : 405-414. doi: 10.3934/krm.2008.1.405
[16]

Casey Jao. Energy-critical NLS with potentials of quadratic growth. Discrete & Continuous Dynamical Systems, 2018, 38 (2) : 563-587. doi: 10.3934/dcds.2018025
[17]

Alessio Figalli, Vito Mandorino. Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials. Discrete & Continuous Dynamical Systems, 2011, 31 (4) : 1325-1346. doi: 10.3934/dcds.2011.31.1325
[18]

Dmitry Dolgopyat. Bouncing balls in non-linear potentials. Discrete & Continuous Dynamical Systems, 2008, 22 (1&2) : 165-182. doi: 10.3934/dcds.2008.22.165
[19]

Cornelis van der Mee. Direct scattering of AKNS systems with $L^2$ potentials. Conference Publications, 2015, 2015 (special) : 1089-1097. doi: 10.3934/proc.2015.1089
[20]

Fei Meng, Fang Liu. On the inelastic Boltzmann equation for soft potentials with diffusion. Communications on Pure & Applied Analysis, 2020, 19 (11) : 5197-5217. doi: 10.3934/cpaa.2020233

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (71)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences