Holdings: Partial inner product spaces

Partial inner product spaces: theory and applications

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Bibliographic Details
Main Authors:	Antoine, Jean-Pierre 1940- (Author), Trapani, Camillo (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2009
Series:	Lecture notes in mathematics 1986
Subjects:	Espaces à produit scalaire Inner product spaces Innenproduktraum
Online Access:	Vorwort 1 Kapitel 1 Inhaltsverzeichnis
Physical Description:	XX, 352 S. graph. Darst. 235 mm x 155 mm
ISBN:	9783642051357

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MARC


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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
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author	Antoine, Jean-Pierre 1940- Trapani, Camillo
author_GND	(DE-588)121807444 (DE-588)140712011
author_facet	Antoine, Jean-Pierre 1940- Trapani, Camillo
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author_sort	Antoine, Jean-Pierre 1940-
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callnumber-first	Q - Science
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classification_rvk	SI 850
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
dewey-search	515.73
dewey-sort	3515.73
dewey-tens	510 - Mathematics
discipline	Mathematik
format	Book
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isbn	9783642051357
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physical	XX, 352 S. graph. Darst. 235 mm x 155 mm
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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
url	http://swbplus.bsz-bw.de/bsz319569136vor.htm http://swbplus.bsz-bw.de/bsz319569136kap.htm 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
volume_link	(DE-604)BV000676446
work_keys_str_mv	AT antoinejeanpierre partialinnerproductspacestheoryandapplications AT trapanicamillo partialinnerproductspacestheoryandapplications

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