Spectral theory of non-commutative harmonic oscillators: an introduction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2010
|
| Series: | Lecture notes in mathematics
1992 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben. - Zusätzliches Online-Angebot unter www.springer.com |
| Physical Description: | XI, 254 S. graph. Darst. |
| ISBN: | 9783642119217 |
Staff View
MARC
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| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XI, 254 S. |b graph. Darst. | ||
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Record in the Search Index
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| adam_text |
CONTENTS 1 INTRODUCTION 1 2 THE HARMONIC OSCILLATOR 7 2. 1 FROM THE
HAMILTONIAN TO THE OPERATOR ACTING ON L 2 7 2.2 THE SPECTRUM OF THE
HARMONIC OSCILLATOR 10 3 THE WEYL-HOERMANDER CALCULUS 15 3.1 REVIEW OF
THE WEYL-HOERMANDER CALCULUS 15 3.2 GLOBAL METRICS AND GLOBAL
PSEUDODIFFERENTIAL OPERATORS 25 3.3 SPECTRAL PROPERTIES OF GLOBALLY
ELLIPTIC PSEUDODIFFERENTIAL OPERATORS 41 3.4 NOTES 53 4 THE SPECTRAL
COUNTING FUNCTION N(X) AND THE BEHAVIOR OF THE EIGENVALUES: PART 1 55
4.1 THE MINIMAX PRINCIPLE 55 4.2 THE SPECTRAL COUNTING FUNCTION 58 4.3
THE SPECTRAL COUNTING FUNCTION OF THE (SCALAR) HARMONIC OSCILLATOR 61
4.4 CONSEQUENCES ON THE SPECTRAL COUNTING FUNCTION OF AN ELLIPTIC GLOBAL
Y/DO 65 5 THE HEAT-SEMIGROUP, FUNCTIONAL CALCULUS AND KERNELS 67 5.1
ELEMENTARY PROPERTIES OF THE HEAT-SEMIGROUP 67 5.2 DIRECT DEFINITION OF
TRE" M 69 5.3 ABSTRACT FUNCTIONAL CALCULUS 71 5.4 KERNELS 73 5.5 * (A)
AS A PSEUDODIFFERENTIAL OPERATOR 77 5.6 NOTES 77 6 THE SPECTRAL COUNTING
FUNCTION N(X) AN BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/1000028399 DIGITALISIERT DURCH X CONTENTS 6.3 USE OF
THE PARAMETRIX APPROXIMATION OF E~' A FOR OBTAINING THE WEYL ASYMPTOTICS
OF N(X) 86 6.4 REMARKS ON THE HEURISTICS ON N(X) AND C A (S) 91 6.5
NOTES 92 7 THE SPECTRAL ZETA FUNCTION 93 7.1 ROBERT'S CONSTRUCTION OF C
A BY COMPLEX POWERS 93 7.2 THE MEROMORPHIC CONTINUATION OF Q VIA THE
PARAMETRIX APPROXIMATION OF E~' A 96 7.3 THE ICHINOSE-WAKAYAMA THEOREM
106 7.4 NOTES 110 8 SOME PROPERTIES OF THE EIGENVALUES OF Q* ASS) (X, D)
ILL 8. 1 THE ICHINOSE AND WAKAYAMA BOUNDS 112 8.2 A BETTER UPPER-BOUND
FOR THE LOWEST EIGENVALUE 115 8.3 NOTES 120 9 SOME TOOLS FROM THE
SEMICIASSICAL CALCULUS 121 9.1 THE SEMICIASSICAL CALCULUS 121 9.2
DECOUPLING A SYSTEM 129 9.3 SOME ESTIMATES FOR SEMICIASSICAL OPERATORS
140 9.4 SOME SPECTRAL PROPERTIES OF SEMICIASSICAL GPDOS 143 10 ON
OPERATORS INDUCED BY GENERAL FINITE-RANK ORTHOGONAL PROJECTIONS 149 10.
CONTENTS XI APPENDIX 239 A.I ALMOST-ANALYTIC EXTENSION AND THE
DYN'KIN-HELFFER- SJOESTRAND FORMULA 239 MAIN NOTATION 245 B. 1 GENERAL
NOTATION 245 B.2 SYMBOL, FUNCTION AND OPERATOR SPACES 246 B.3 THE
SPECTRAL COUNTING FUNCTION AND THE SPECTRAL ^-FUNCTION 247 B.4 DYNAMICAL
QUANTITIES AND ASSUMPTIONS 247 B.5 CLASSES OF SYSTEMS 247 REFERENCES 249
INDEX 253 |
| any_adam_object | 1 |
| author | Parmeggiani, Alberto 1963- |
| author_GND | (DE-588)141266015 |
| author_facet | Parmeggiani, Alberto 1963- |
| author_role | aut |
| author_sort | Parmeggiani, Alberto 1963- |
| author_variant | a p ap |
| building | Verbundindex |
| bvnumber | BV036516212 |
| classification_rvk | SI 850 |
| classification_tum | MAT 470f MAT 342f |
| ctrlnum | (OCoLC)637028768 (DE-599)DNB1000028399 |
| dewey-full | 515.7242 515.3533 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7242 515.3533 |
| dewey-search | 515.7242 515.3533 |
| dewey-sort | 3515.7242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 9783642119217 |
| language | English |
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| physical | XI, 254 S. graph. Darst. |
| publishDate | 2010 |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Parmeggiani, Alberto 1963- Verfasser (DE-588)141266015 aut Spectral theory of non-commutative harmonic oscillators an introduction Alberto Parmeggiani Berlin [u.a.] Springer 2010 XI, 254 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1992 Literaturangaben. - Zusätzliches Online-Angebot unter www.springer.com Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Harmonischer Oszillator (DE-588)4159128-8 gnd rswk-swf Harmonischer Oszillator (DE-588)4159128-8 s Spektraltheorie (DE-588)4116561-5 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-11922-4 Lecture notes in mathematics 1992 (DE-604)BV000676446 1992 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3423087&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020438322&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Parmeggiani, Alberto 1963- Spectral theory of non-commutative harmonic oscillators an introduction Lecture notes in mathematics Spektraltheorie (DE-588)4116561-5 gnd Harmonischer Oszillator (DE-588)4159128-8 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4159128-8 |
| title | Spectral theory of non-commutative harmonic oscillators an introduction |
| title_auth | Spectral theory of non-commutative harmonic oscillators an introduction |
| title_exact_search | Spectral theory of non-commutative harmonic oscillators an introduction |
| title_full | Spectral theory of non-commutative harmonic oscillators an introduction Alberto Parmeggiani |
| title_fullStr | Spectral theory of non-commutative harmonic oscillators an introduction Alberto Parmeggiani |
| title_full_unstemmed | Spectral theory of non-commutative harmonic oscillators an introduction Alberto Parmeggiani |
| title_short | Spectral theory of non-commutative harmonic oscillators |
| title_sort | spectral theory of non commutative harmonic oscillators an introduction |
| title_sub | an introduction |
| topic | Spektraltheorie (DE-588)4116561-5 gnd Harmonischer Oszillator (DE-588)4159128-8 gnd |
| topic_facet | Spektraltheorie Harmonischer Oszillator |
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| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT parmeggianialberto spectraltheoryofnoncommutativeharmonicoscillatorsanintroduction |