Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, R.I.
American Math. Soc.
1987
|
| Series: | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics
171 = 1987,2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | VI, 121 S. graph. Darst. |
| ISBN: | 0821831046 |
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| 240 | 1 | 0 | |a Geometričeskie i arifmetičeskie metody v spektral'noj teorii mnogomernych periodičeskich operatorov |
| 245 | 1 | 0 | |a Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators |c by M. M. Skriganov |
| 264 | 1 | |a Providence, R.I. |b American Math. Soc. |c 1987 | |
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| 650 | 4 | |a Geometry of numbers | |
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Record in the Search Index
| _version_ | 1804118004445741056 |
|---|---|
| adam_text | CONTENTS
Introduction 1
CHAPTER I. Preliminaries 11
§1. Facts from the geometry of numbers 11
§2. Periodic functions 15
§3. The number of lattice points in multidimensional regions 19
§4. Periodic operators 23
§5. Some results in perturbation theory 27
CHAPTER II. General properties of the band structure of the spectra of pe¬
riodic operators. Brillouin zones 31
§6. The band structure of the spectrum and the eigenfunction expansion
theorem for a periodic operator 31
§7. Deformations of the band structure. Stability of points in the spec¬
trum. The common spectrum 37
§8. Definition and basic properties of Brillouin zones 43
§9. Brillouin zones and the unperturbed band structure of the spectrum 49
§10. Brillouin zones from the point of view of the geometry of numbers. 52
CHAPTER HI. Structure of the spectrum of certain periodic operators .... 59
§11. Simplest properties of the spectrum of a multidimensional
Schrodinger operator with periodic potential 59
§12. Two dimensional periodic Schrodinger operators 64
§13. Periodic operators with strongly convex symbol 70
§14. Polyharmonic operators with periodic perturbation 73
§15. The empty shell method. Periodic Schrodinger operators in dimen¬
sions greater than two 77
CHAPTER IV. The band structure of the spectrum of a multidimensional
Schrodinger operator with local periodic potential 89
§16. Statements of the main results 89
§17. Additional facts about rational lattices 91
§18. Specialization of the period lattice and of the form of the potential.
Multiplicity of the covering by unperturbed bands of the spectrum 98
§19. The modified empty shell method. 1 106
§20. The modified empty shell method. 2. Proofs of the main results . . Ill
Bibliography 117
V
|
| any_adam_object | 1 |
| author | Skriganov, M. M. |
| author_facet | Skriganov, M. M. |
| author_role | aut |
| author_sort | Skriganov, M. M. |
| author_variant | m m s mm mms |
| building | Verbundindex |
| bvnumber | BV003656114 |
| callnumber-first | Q - Science |
| callnumber-label | QA1 |
| callnumber-raw | QA1 |
| callnumber-search | QA1 |
| callnumber-sort | QA 11 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 700 |
| ctrlnum | (OCoLC)260191668 (DE-599)BVBBV003656114 |
| dewey-full | 510 512/.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 512 - Algebra |
| dewey-raw | 510 512/.72 |
| dewey-search | 510 512/.72 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV003656114 |
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| indexdate | 2024-07-09T16:03:24Z |
| institution | BVB |
| isbn | 0821831046 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002328200 |
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| physical | VI, 121 S. graph. Darst. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics |
| series2 | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics |
| spelling | Skriganov, M. M. Verfasser aut Geometričeskie i arifmetičeskie metody v spektral'noj teorii mnogomernych periodičeskich operatorov Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators by M. M. Skriganov Providence, R.I. American Math. Soc. 1987 VI, 121 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics 171 = 1987,2 Aus d. Russ. übers. Analise De Series Temporais larpcal Géométrie des nombres Operadores (Analise Funcional) larpcal Schrödinger, Opérateur de Spectre (Mathématiques) Équations différentielles elliptiques Differential equations, Elliptic Geometry of numbers Schrödinger operator Spectral theory (Mathematics) Hamilton-Operator (DE-588)4072278-8 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Spektraltheorie (DE-588)4116561-5 s Hamilton-Operator (DE-588)4072278-8 s Elliptische Differentialgleichung (DE-588)4014485-9 s DE-604 Quantenmechanik (DE-588)4047989-4 s 2\p DE-604 Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics 171 = 1987,2 (DE-604)BV000009943 171 = 1987,2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002328200&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Skriganov, M. M. Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics Analise De Series Temporais larpcal Géométrie des nombres Operadores (Analise Funcional) larpcal Schrödinger, Opérateur de Spectre (Mathématiques) Équations différentielles elliptiques Differential equations, Elliptic Geometry of numbers Schrödinger operator Spectral theory (Mathematics) Hamilton-Operator (DE-588)4072278-8 gnd Spektraltheorie (DE-588)4116561-5 gnd Quantenmechanik (DE-588)4047989-4 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| subject_GND | (DE-588)4072278-8 (DE-588)4116561-5 (DE-588)4047989-4 (DE-588)4014485-9 (DE-588)4143413-4 |
| title | Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators |
| title_alt | Geometričeskie i arifmetičeskie metody v spektral'noj teorii mnogomernych periodičeskich operatorov |
| title_auth | Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators |
| title_exact_search | Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators |
| title_full | Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators by M. M. Skriganov |
| title_fullStr | Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators by M. M. Skriganov |
| title_full_unstemmed | Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators by M. M. Skriganov |
| title_short | Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators |
| title_sort | geometric and arithmetic methods in the spectral theory of multidimensional periodic operators |
| topic | Analise De Series Temporais larpcal Géométrie des nombres Operadores (Analise Funcional) larpcal Schrödinger, Opérateur de Spectre (Mathématiques) Équations différentielles elliptiques Differential equations, Elliptic Geometry of numbers Schrödinger operator Spectral theory (Mathematics) Hamilton-Operator (DE-588)4072278-8 gnd Spektraltheorie (DE-588)4116561-5 gnd Quantenmechanik (DE-588)4047989-4 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| topic_facet | Analise De Series Temporais Géométrie des nombres Operadores (Analise Funcional) Schrödinger, Opérateur de Spectre (Mathématiques) Équations différentielles elliptiques Differential equations, Elliptic Geometry of numbers Schrödinger operator Spectral theory (Mathematics) Hamilton-Operator Spektraltheorie Quantenmechanik Elliptische Differentialgleichung Aufsatzsammlung |
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