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Extended states for the Schrödinger operator with quasi-periodic potential in dimension two /
The authors consider a Schrödinger operator H=-\Delta +V(\vec x) in dimension two with a quasi-periodic potential V(\vec x). They prove that the absolutely continuous spectrum of H contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the follo...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, RI :
American Mathematical Society,
2019.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1239. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title page; Chapter 1. Introduction; Chapter 2. Preliminary Remarks; Chapter 3. Step I; 3.1. The Operator ⁽¹⁾; 3.2. Perturbation Formulas; 3.3. Geometric Considerations; 3.4. Isoenergetic Surface for the Operator ⁽¹⁾; 3.5. Preparation for Step II. Construction of the Second Nonresonant Set; Chapter 4. Step II; 4.1. The Operator ⁽²⁾. Perturbation Formulas; 4.2. Isoenergetic Surface for the Operator ⁽²⁾; 4.3. Preparation for Step III
- Geometric Part. Properties of the Quasiperiodic Lattice; 4.4. Preparation for Step III
- Analytic Part; Chapter 5. Step III
- 5.1. The Operator ⁽³⁾. Perturbation Formulas5.2. Isoenergetic Surface for the Operator ⁽³⁾; 5.3. Preparation for Step IV; Chapter 6. STEP IV; 6.1. The Operator ⁽⁴⁾. Perturbation Formulas; 6.2. Isoenergetic Surface for the Operator ⁽⁴⁾; Chapter 7. Induction; 7.1. Inductive formulas for _{ }; 7.2. Preparation for Step +1, ≥4; 7.3. The Operator ⁽ⁿ⁺¹⁾. Perturbation Formulas; 7.4. Isoenergetic Surface for the Operator ⁽ⁿ⁺¹⁾; Chapter 8. Isoenergetic Sets. Generalized Eigenfunctions of; 8.1. Construction of the Limit-Isoenergetic Set; 8.2. Generalized Eigenfunctions of
- Chapter 9. Proof of Absolute Continuity of the Spectrum9.1. The Operators _{ }( _{ }'), _{ }'⊂ _{ }; 9.2. Sets _{∞} and _{∞, }; 9.3. Projections ( _{∞, }); 9.4. Proof of Absolute Continuity; Chapter 10. Appendices; 10.1. Appendix 1. Proof of Lemma 3.12; 10.2. Appendix 2. Proof of Lemma 3.13; 10.3. Appendix 3; 10.4. Appendix 4; 10.5. Appendix 5; 10.6. Appendix 6; 10.7. Appendix 7; 10.8. Appendix 8. An Application of Bezout's Theorem; 10.9. Appendix 9. On the Proof of Geometric Lemmas Allowing to Deal with Clusters instead of Boxes; 10.10. Appendix 10
- Chapter 11. List of main notationsBibliography; Back Cover