Partial inner product spaces: theory and applications
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2009
|
| Schriftenreihe: | Lecture notes in mathematics
1986 |
| Schlagworte: | |
| Online-Zugang: | Vorwort 1 Kapitel 1 Inhaltsverzeichnis |
| Beschreibung: | XX, 352 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9783642051357 |
Internformat
MARC
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| 100 | 1 | |a Antoine, Jean-Pierre |d 1940- |e Verfasser |0 (DE-588)121807444 |4 aut | |
| 245 | 1 | 0 | |a Partial inner product spaces |b theory and applications |c Jean-Pierre Antoine ; Camillo Trapani |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a XX, 352 S. |b graph. Darst. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1986 | |
| 650 | 4 | |a Espaces à produit scalaire | |
| 650 | 4 | |a Inner product spaces | |
| 650 | 0 | 7 | |a Innenproduktraum |0 (DE-588)4130366-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Innenproduktraum |0 (DE-588)4130366-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Trapani, Camillo |e Verfasser |0 (DE-588)140712011 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-642-05136-4 |
| 830 | 0 | |a Lecture notes in mathematics |v 1986 |w (DE-604)BV000676446 |9 1986 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-018967690 | ||
Datensatz im Suchindex
| _version_ | 1804141131029544960 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
INTRODUCTION 1
1 BACKGROUND ON DIFFERENTIAL GEOMETRY 13
1.1 FIBRE BUNDLES AND CONNECTIONS 13
1.2 RIEMANNIAN MANIFOLDS 31
1.3 SUPERSPACES 37
1.4 SUPERCONNECTIONS 41
1.5 CHARACTERISTIC CLASSES 44
1.6 THE EULER AND THORN CLASSES 49
2 ASYMPTOTIC EXPANSION OF THE HEAT KERNEL 61
2.1 DIFFERENTIAL OPERATORS 62
2.2 THE HEAT KERNEL ON EUCLIDEAN SPACE 69
2.3 HEAT KERNELS 71
2.4 CONSTRUCTION OF THE HEAT KERNEL 74
2.5 THE FORMAL SOLUTION 79
2.6 THE TRACE OF THE HEAT KERNEL 85
2.7 HEAT KERNELS DEPENDING ON A PARAMETER 95
3 CLIFFORD MODULES AND DIRAC OPERATORS 99
3.1 THE CLIFFORD ALGEBRA 100
3.2 SPINORS 106
3.3 DIRAC OPERATORS 110
3.4 INDEX OF DIRAC OPERATORS 118
3.5 THE LICHNEROWICZ FORMULA 122
3.6 SOME EXAMPLES OF CLIFFORD MODULES 123
4 INDEX DENSITY OF DIRAC OPERATORS 139
4.1 THE LOCAL INDEX THEOREM 139
4.2 MEHLER S FORMULA 149
4.3 CALCULATION OF THE INDEX DENSITY 153
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/996813551
DIGITALISIERT DURCH
IMAGE 2
VIII CONTENTS
5 THE EXPONENTIAL MAP AND THE INDEX DENSITY 163
5.1 JACOBIAN OF THE EXPONENTIAL MAP ON PRINCIPAL BUNDLES 164 5.2 THE
HEAT KERNEL OF A PRINCIPAL BUNDLE 168
5.3 CALCULUS WITH GRASSMANN AND CLIFFORD VARIABLES 173
5.4 THE INDEX OF DIRAC OPERATORS 177
6 THE EQUIVARIANT INDEX THEOREM 181
6.1 THE EQUIVARIANT INDEX OF DIRAC OPERATORS 182
6.2 THE ATIYAH-BOTT FIXED POINT FORMULA 183
6.3 ASYMPTOTIC EXPANSION OF THE EQUIVARIANT HEAT KERNEL 187 6.4 THE
LOCAL EQUIVARIANT INDEX THEOREM 190
6.5 GEODESIC DISTANCE ON A PRINCIPAL BUNDLE 194
6.6 THE HEAT KERNEL OF AN EQUIVARIANT VECTOR BUNDLE 196
6.7 PROOF OF PROPOSITION 6.13 199
7 EQUIVARIANT DIFFERENTIAL FORMS 203
7.1 EQUIVARIANT CHARACTERISTIC CLASSES 204
7.2 THE LOCALIZATION FORMULA 211
7.3 BOTT S FORMULAS FOR CHARACTERISTIC NUMBERS 219
7.4 EXACT STATIONARY PHASE APPROXIMATION 221
7.5 THE FOURIER TRANSFORM OF COADJOINT ORBITS 223
7.6 EQUIVARIANT COHOMOLOGY AND FAMILIES 229
7.7 THE BOTT CLASS 236
8 THE KIRILLOV FORMULA FOR THE EQUIVARIANT INDEX 243
8.1 THE KIRILLOV FORMULA 244
8.2 THE WEYL AND KIRILLOV CHARACTER FORMULAS 248
8.3 THE HEAT KERNEL PROOF OF THE KIRILLOV FORMULA 252
9 THE INDEX BUNDLE 263
9.1 THE INDEX BUNDLE IN FINITE DIMENSIONS 265
9.2 THE INDEX BUNDLE OF A FAMILY OF DIRAC OPERATORS 273
9.3 THE CHERN CHARACTER OF THE INDEX BUNDLE 276
9.4 THE EQUIVARIANT INDEX AND THE INDEX BUNDLE 287
9.5 THE CASE OF VARYING DIMENSION 289
9.6 THEZETA-FUNCTIONOFALAPLACIAN 293
9.7 THE DETERMINANT LINE BUNDLE 298
10 THE FAMILY INDEX THEOREM 311
10.1 RIEMANNIAN FIBRE BUNDLES 314
10.2 CLIFFORD MODULES ON FIBRE BUNDLES 319
10.3 THE BISMUT SUPERCONNECTION 326
10.4 THE FAMILY INDEX DENSITY 330
10.5 THE TRANSGRESSION FORMULA 338
10.6 THE CURVATURE OF THE DETERMINANT LINE BUNDLE 341
10.7 THE KIRILLOV FORMULA AND BISMUT S INDEX THEOREM 344
IMAGE 3
CONTENTS IX
REFERENCES 349
LIST OF NOTATION 355
INDEX 359
|
| any_adam_object | 1 |
| author | Antoine, Jean-Pierre 1940- Trapani, Camillo |
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| classification_tum | MAT 462f MAT 463f |
| ctrlnum | (OCoLC)568790644 (DE-599)DNB996813551 |
| dewey-full | 515.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.73 |
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| discipline | Mathematik |
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| isbn | 9783642051357 |
| language | English |
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| physical | XX, 352 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2009 |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Antoine, Jean-Pierre 1940- Verfasser (DE-588)121807444 aut Partial inner product spaces theory and applications Jean-Pierre Antoine ; Camillo Trapani Berlin [u.a.] Springer 2009 XX, 352 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1986 Espaces à produit scalaire Inner product spaces Innenproduktraum (DE-588)4130366-0 gnd rswk-swf Innenproduktraum (DE-588)4130366-0 s DE-604 Trapani, Camillo Verfasser (DE-588)140712011 aut Erscheint auch als Online-Ausgabe 978-3-642-05136-4 Lecture notes in mathematics 1986 (DE-604)BV000676446 1986 DE-576;springer application/pdf http://swbplus.bsz-bw.de/bsz319569136vor.htm 20100308114317 Vorwort 1 DE-576;springer application/pdf http://swbplus.bsz-bw.de/bsz319569136kap.htm 20100308115050 Kapitel 1 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018967690&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Antoine, Jean-Pierre 1940- Trapani, Camillo Partial inner product spaces theory and applications Lecture notes in mathematics Espaces à produit scalaire Inner product spaces Innenproduktraum (DE-588)4130366-0 gnd |
| subject_GND | (DE-588)4130366-0 |
| title | Partial inner product spaces theory and applications |
| title_auth | Partial inner product spaces theory and applications |
| title_exact_search | Partial inner product spaces theory and applications |
| title_full | Partial inner product spaces theory and applications Jean-Pierre Antoine ; Camillo Trapani |
| title_fullStr | Partial inner product spaces theory and applications Jean-Pierre Antoine ; Camillo Trapani |
| title_full_unstemmed | Partial inner product spaces theory and applications Jean-Pierre Antoine ; Camillo Trapani |
| title_short | Partial inner product spaces |
| title_sort | partial inner product spaces theory and applications |
| title_sub | theory and applications |
| topic | Espaces à produit scalaire Inner product spaces Innenproduktraum (DE-588)4130366-0 gnd |
| topic_facet | Espaces à produit scalaire Inner product spaces Innenproduktraum |
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