Extended States for the Schrödinger Operator with Quasi-Periodic Potential in Dimension Two. (Record no. 10471)
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| fixed length control field | 04870nam a22004693i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC5770285 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240724113716.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2019 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470450694 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470435431 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC5770285 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL5770285 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1096296267 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QC174.17.S3 .K377 2019 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 530.12/4 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Karpeshina, Yulia. |
| 245 10 - TITLE STATEMENT | |
| Title | Extended States for the Schrödinger Operator with Quasi-Periodic Potential in Dimension Two. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2019. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2019. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (152 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.258 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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 Formulas -- 5.2. 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 Spectrum -- 9.1. 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 notations. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Bibliography -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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 (Cantor type structure). A new method of multiscale analysis in the momentum space is developed to prove these results. The result is based on a previous paper on the quasiperiodic polyharmonic operator (-\Delta )^l+V(\vec x), l>1. Here the authors address technical complications arising in the case l=1. However, this text is self-contained and can be read without familiarity with the previous paper. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Schrödinger equation. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Shterenberg, Roman. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Karpeshina, Yulia |
| Title | Extended States for the Schrödinger Operator with Quasi-Periodic Potential in Dimension Two |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2019 |
| International Standard Book Number | 9781470435431 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5770285">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5770285</a> |
| Public note | Click to View |
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