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

Remarks on a paper of Kotani concerning generalized reflectionless Schrödinger potentials

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.
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]

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

[4]

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

[5]

Ruikuan Liu, Tian Ma, Shouhong Wang, Jiayan Yang. Thermodynamical potentials of classical and quantum systems. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-38. doi: 10.3934/dcdsb.2018214

[6]

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

[7]

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

[8]

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

[9]

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

[10]

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

[11]

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

[12]

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

[13]

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

[14]

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

[15]

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

[16]

Dongsheng Kang. Quasilinear systems involving multiple critical exponents and potentials. Communications on Pure & Applied Analysis, 2013, 12 (2) : 695-710. doi: 10.3934/cpaa.2013.12.695

[17]

Maurizio Grasselli, Giulio Schimperna. Nonlocal phase-field systems with general potentials. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5089-5106. doi: 10.3934/dcds.2013.33.5089

[18]

Yongluo Cao, De-Jun Feng, Wen Huang. The thermodynamic formalism for sub-additive potentials. Discrete & Continuous Dynamical Systems - A, 2008, 20 (3) : 639-657. doi: 10.3934/dcds.2008.20.639

[19]

Julien Barral, Yan-Hui Qu. Localized asymptotic behavior for almost additive potentials. Discrete & Continuous Dynamical Systems - A, 2012, 32 (3) : 717-751. doi: 10.3934/dcds.2012.32.717

[20]

Yutian Lei. Positive solutions of integral systems involving Bessel potentials. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2721-2737. doi: 10.3934/cpaa.2013.12.2721

2017 Impact Factor: 0.972

Metrics

  • PDF downloads (3)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]