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We consider the operator $\mathcal{A}_h = -h^2 \Delta + iV$ in the semi-classical limit $h \to 0$, where $V$ is a smooth real potential with no critical points. We obtain both the left margin of the spectrum, as well as resolvent estimates on the left side of this margin. We extend here previous results obtained for the Dirichlet realization of $\mathcal{A}_h$ by removing significant limitations that were formerly imposed on $V$. In addition, we apply our techniques to the more general Robin boundary condition and to a transmission problem which is of significant interest in physical applications. We consider the operator $\mathcal{A}_h = -h^2 \Delta + iV$ in the semi-classical limit $h \to 0$, where $V$ is a smooth real potential with no critical points. We obtain both the left margin of the spectrum, as well as resolvent estimates on the left side of this margin. We extend here previous results obtained for the Dirichlet realization of $\mathcal{A}_h$ by removing significant limitations that were formerly imposed on $V$. In addition, ...

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Documents 47A10 | enregistrements trouvés : 81

Spectral theory and semi-classical analysis for the complex Schrödinger operator Helffer, Bernard | CIRM H Nouveau

Spectral theory and applications :CRM summer school on spectral theory and applicationsQuébec # July 4-14, 2016 Girouard, Alexandre | American Mathematical Society 2018 Nouveau

Operator theory in different settings and related applications :26th international workshop on operator theory and its applications (IWOTA) Tbilisi # July 6-10, 2015 Duduchava, Roland ; Kaashoek, Marinus A. ; Vasilevski, Nikolai L. ; Vinnikov, Victor | Birkhäuser 2018 Nouveau

The diversity and beauty of applied operator theory.Proceedings of the 28th international workshop on operator theory and its applications (IWOTA)Chemnitz # August 14-18, 2017 Böttcher, Albrecht ; Potts, Daniel ; Stollmann, Peter ; Wenzel, David | Birkhäuser 2018 Nouveau

Actes du 1er congrès national de la SMF :Tours # 6-10 juin 2016 Lecouvey, Cédric | Société Mathématique de France 2017 Nouveau

Evolution equations of hyperbolic and Schrödinger type:asymptotics, estimates and nonlinearities.Based on a workshop on asymptotic properties of solutions to hyperbolic equationsLondon # March 2011 Ruzhansky, Michael ; Sugimoto, Mitsuru ; Wirth, Jens | Birkhäuser 2012 Nouveau

Operator theory in harmonic and non-commutative analysis.23rd international workshop in operator theory and its applicationsSydney # july 2012 Ball, Joseph A. ; Dritschel, Michael A. ; Ter Elst, A. F. M. ; Portal, Pierre ; Potapov, Denis | Birkhäuser 2014 Nouveau

Pseudo-differential operators, generalized functions and asymptotics.Selected papers of the 8th ISAAC congressMoscow # august 22-27, 2011 Molahajloo, Shahla ; Pilipovic, Stevan ; Toft, Joachim ; Wong, M. W. | Birkhäuser 2013 Nouveau

Recent developments in fractals and related fields.Based on the international conference on fractals and related fields, held in honor of Jacques PeyrièreMonastir # september 2007 Barral, Julien ; Seuret, Stéphane | Birkhäuser 2010 Nouveau

Pseudo-differential operators: analysis, applications and computations.Selected papers based on lectures presented at the meeting of the ISAAC group in pseudo-differential operators (IGPDO)London # july 13-18, 2009 Rodino, Luigi ; Wong, Man W. ; Zhu, Hongmei | Birkhäuser 2011 Nouveau

Elementary operators and their applications.3rd international workshopBelfast # april, 14-17, 2009 Curto, Raul E. ; Mathieu, Martin | Birkhäuser 2011 Nouveau

Recent advances in operator theory and applications:proceedings of IWOTA#July31-Aug.3 Ando, T. ; Curto, Raul E. ; Jung, Il Bong ; Lee, Woo Young | Birkhäuser Verlag 2009 Nouveau

Séminaire "les semi-groupes et les équations d'évolution" année 1972-73, 1973-74 Damlamian, Alain ; Hirsch, Francis ; Picard , Colette ; Attouch, Hedy | Université Paris XI U.E.R. mathématique 1972 Nouveau

Function spaces :fourth conference on ... held at Southern Illinois University#May 14-19 Jarosz, Krzysztof | American Mathematical Society 2003 Nouveau

Séminaire sur les équations aux dérivées partielles II TIT2 partie 3 Combet, E. ; Vaillant, J. ; Zerner, M. | Collège de France 1964 Nouveau

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Spectral theory and applications :
CRM summer school on spectral theory and applications
Québec # July 4-14, 2016 Girouard, Alexandre | American Mathematical Society 2018 Nouveau

Operator theory in different settings and related applications :
26th international workshop on operator theory and its applications (IWOTA) Tbilisi # July 6-10, 2015 Duduchava, Roland ; Kaashoek, Marinus A. ; Vasilevski, Nikolai L. ; Vinnikov, Victor | Birkhäuser 2018 Nouveau

The diversity and beauty of applied operator theory.
Proceedings of the 28th international workshop on operator theory and its applications (IWOTA)
Chemnitz # August 14-18, 2017 Böttcher, Albrecht ; Potts, Daniel ; Stollmann, Peter ; Wenzel, David | Birkhäuser 2018 Nouveau

Actes du 1er congrès national de la SMF :
Tours # 6-10 juin 2016 Lecouvey, Cédric | Société Mathématique de France 2017 Nouveau

Evolution equations of hyperbolic and Schrödinger type:
asymptotics, estimates and nonlinearities.
Based on a workshop on asymptotic properties of solutions to hyperbolic equations
London # March 2011 Ruzhansky, Michael ; Sugimoto, Mitsuru ; Wirth, Jens | Birkhäuser 2012 Nouveau

Operator theory in harmonic and non-commutative analysis.
23rd international workshop in operator theory and its applications
Sydney # july 2012 Ball, Joseph A. ; Dritschel, Michael A. ; Ter Elst, A. F. M. ; Portal, Pierre ; Potapov, Denis | Birkhäuser 2014 Nouveau

Pseudo-differential operators, generalized functions and asymptotics.
Selected papers of the 8th ISAAC congress
Moscow # august 22-27, 2011 Molahajloo, Shahla ; Pilipovic, Stevan ; Toft, Joachim ; Wong, M. W. | Birkhäuser 2013 Nouveau

Recent developments in fractals and related fields.
Based on the international conference on fractals and related fields, held in honor of Jacques Peyrière
Monastir # september 2007 Barral, Julien ; Seuret, Stéphane | Birkhäuser 2010 Nouveau

Pseudo-differential operators: analysis, applications and computations.
Selected papers based on lectures presented at the meeting of the ISAAC group in pseudo-differential operators (IGPDO)
London # july 13-18, 2009 Rodino, Luigi ; Wong, Man W. ; Zhu, Hongmei | Birkhäuser 2011 Nouveau

Elementary operators and their applications.
3rd international workshop
Belfast # april, 14-17, 2009 Curto, Raul E. ; Mathieu, Martin | Birkhäuser 2011 Nouveau

Recent advances in operator theory and applications:
proceedings of IWOTA#July31-Aug.3 Ando, T. ; Curto, Raul E. ; Jung, Il Bong ; Lee, Woo Young | Birkhäuser Verlag 2009 Nouveau

Function spaces :
fourth conference on ... held at Southern Illinois University#May 14-19 Jarosz, Krzysztof | American Mathematical Society 2003 Nouveau