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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 |
MARC
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| 001 | EBOOKCENTRAL_on1096296267 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
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| 019 | |a 1101194134 | ||
| 020 | |a 9781470450694 |q (ebook) | ||
| 020 | |a 1470450690 |q (ebook) | ||
| 020 | |z 9781470435431 |q (alk. paper) | ||
| 020 | |z 1470435438 |q (alk. paper) | ||
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| 050 | 4 | |a QC174.17.S3 |b K37 2019 | |
| 082 | 0 | 4 | |a 530.12/4 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Karpeshina, Yulia E., |d 1956- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjKcp9pf6WkqHRftRp36Dq | |
| 245 | 1 | 0 | |a Extended states for the Schrödinger operator with quasi-periodic potential in dimension two / |c Yulia Karpeshina, Roman Shterenberg. |
| 264 | 1 | |a Providence, RI : |b American Mathematical Society, |c 2019. | |
| 264 | 4 | |c ©2019 | |
| 300 | |a 1 online resource (v, 139 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 0065-9266 ; |v number 1239 | |
| 504 | |a Includes bibliographical references. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a Chapter 11. List of main notationsBibliography; Back Cover | |
| 520 | |a 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 following properties. First, the eigenfunctions are close to plane waves e^i\langle \vec \varkappa, \vec x\rangle in the high energy region. Second, the isoenergetic curves in the space of momenta \vec \varkappa corresponding to these eigenfunctions have the form of slightly distorted circles with holes. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Schrödinger equation. | |
| 650 | 6 | |a Équation de Schrödinger. | |
| 650 | 0 | 7 | |a Schrödinger, Ecuación de |2 embucm |
| 650 | 7 | |a Schrödinger equation |2 fast | |
| 700 | 1 | |a Shterenberg, Roman |q (Roman G.), |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjBFhhwhw6rpHxQprvtfC3 | |
| 758 | |i has work: |a Extended states for the Schrödinger operator with quasi-periodic potential in dimension two (Text) |1 https://id.oclc.org/worldcat/entity/E39PCH7tvYpVTYRXCTDjGr8q6X |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: Karpeshina, Yulia E., 1956- |t Extended states for the Schrödinger operator with quasi-periodic potential in dimension two. |d Providence, RI : American Mathematical Society, [2019] |z 9781470435431 |w (DLC) 2019012338 |w (OCoLC)1079399367 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1239. |x 0065-9266 | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=5770285 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH37445244 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL5770285 | ||
| 994 | |a 92 |b IZTAP | ||