Verfügbarkeit: An introduction to involutive structures

An introduction to involutive structures:

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Bibliographische Detailangaben
Hauptverfasser:	Berhanu, Shiferaw (VerfasserIn), Cordaro, Paulo D. (VerfasserIn), Hounie, Jorge (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Cambridge [u.a.] Cambridge Univ. Press 2008
Ausgabe:	1. publ.
Schriftenreihe:	New mathematical monographs 6
Schlagworte:	Approximation theory Bivectors Differential equations, Partial Vector fields Partielle Differentialgleichung Approximationstheorie Vektorfeld
Online-Zugang:	Inhaltsverzeichnis Inhaltsverzeichnis
Beschreibung:	Literaturverz. S. 381 - 389
Beschreibung:	XII, 392 S.
ISBN:	9780521878579 0521878578

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adam_text	AN INTRODUCTION TO INVOLUTIVE STRUCTURES SHIFERAW BERHANU TEMPLE UNIVERSITY PAULO D. CORDARO UNIVERSITY OF SAO PAULO JORGE HOUNIE FEDERAL UNIVERSITY OF SAO CARLOS CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE PAGE IX I LOCALLY INTEGRABLE STRUCTURES 1 1.1 COMPLEX VECTOR FIELDS - 1 1.2 THE ALGEBRAIC STRUCTURE OF X(L) 4 1.3 FORMALLY INTEGRABLE STRUCTURES 5 1.4 DIFFERENTIAL FORMS 7 1.5 THE FROBENIUS THEOREM . 11 1.6 ANALYTIC STRUCTURES , * 14 1.7 THE CHARACTERISTIC SET . . 15 1.8 SOME SPECIAL STRUCTURES 15 1.9 LOCALLY INTEGRABLE STRUCTURES .-.., 19 1.10 LOCAL GENERATORS 21 1.11 LOCAL GENERATORS IN ANALYTIC STRUCTURES. . . 25 1.12 INTEGRABILITY OF COMPLEX AND ELLIPTIC STRUCTURES 26 1.13 ELLIPTIC STRUCTURES IN THE REAL PLANE 28 1.14 COMPATIBLE SUBMANIFOLDS -32 1.15 LOCALLY INTEGRABLE CR STRUCTURES - 36 1.16 A CR STRUCTURE THAT IS NOT LOCALLY INTEGRABLE 38 1.17 THE LEVI FORM ON A FORMALLY IHTEGRABLE STRUCTURE 42 APPENDIX: PROOF OF THE NEWLANDER-NIRENBERG THEOREM 47 NOTES 51 II THE BAOUENDI-TREVES APPROXIMATION FORMULA 52 II. 1 THE APPROXIMATION THEOREM 52 11.2 DISTRIBUTION SOLUTIONS 63 11.3 CONVERGENCE IN STANDARD FUNCTIONAL SPACES 69 11.4 APPLICATIONS 83 N O T E S * * *** * * * * * - * 99 VI CONTENTS Y III SUSSMANN S ORBITS AND UNIQUE CONTINUATION 101 111.1 SUSSMANN S ORBITS 101 111.2 PROPAGATION OF SUPPORT AND GLOBAL UNIQUE CONTINUATION 108 111.3 THE STRONG UNIQUENESS PROPERTY FOR LOCALLY INTEGRABLE SOLUTIONS 120 111.4 PROOF OF THEOREM III.3.15 126 111.5 UNIQUENESS FOR APPROXIMATE SOLUTIONS 132 111.6 REAL-ANALYTIC STRUCTURES IN THE PLANE 140 111.7 FURTHER APPLICATIONS OF SUSSMANN S ORBITS 146 NOTES 147 IV LOCAL SOLVABILITY OF VECTOR FIELDS IV. 1 PLANAR VECTOR FIELDS * * IV.2 SOLVABILITY IN C IV.3 VECTOR FIELDS IN SEVERAL VARIABLES , . * . ; IV.4 NECESSARY CONDITIONS FOR LOCAL SOLVABILITY * NOTES * * ; * - * * , * * : . * . . . * . . . * : V THE FBI TRANSFORM AND SOME APPLICATIONS V. 1 CERTAIN SUBMANIFOLDS OF HYPOANALYTIC MANIFOLDS V.2 MICROLOCAL ANALYTICITY AND THE FBI TRANSFORM V.3 MICROLOCAL SMOOTHNESS V.4 MICROLOCAL HYPOANALYTICITY AND THE FBI TRANSFORM V.5 APPLICATION OF THE FBI TRANSFORM TO THE C 30 WAVE FRONT SET OF SOLUTIONS OF NONLINEAR PDES V.6 APPLICATIONS TO EDGE-OF-THE-WEDGE THEORY V.7 APPLICATION TO THE F. AND M. RIESZ THEOREM N O T E S * : * * . * * VI SOME BOUNDARY PROPERTIES OF SOLUTIONS ..,. , 271 VI. 1 EXISTENCE OF A BOUNDARY VALUE , , . . , * 271 VI.2 POINTWISE, CONVERGENCE TO THE BOUNDARY VALUE . , ; 281 VI.3 ONE-SIDED LOCAL SOLVABILITY IN THE PLANE , .-. .. 286 VI.4 THE// . PROPERTY FOR VECTOR FIELDS . . . 289 NOTES 307 VII THE DIFFERENTIAL COMPLEX ASSOCIATED WITH A FORMALLY F , INTEGRABLE STRUCTURE ...,,, , 308 . VII.L THE EXTERIOR DERIVATIVE . ... .., ; : . . ,308 VII.2 THE LOCAL REPRESENTATION .OF THE EXTERIOR, DERIVATIVE -. . ,309 VII.3 THE POINCARE LEMMA ., , , , - 311 VII.4 THE DIFFERENTIAL COMPLEX ASSOCIATED WITH A FORMALLY INTEGRABLE STRUCTURE 3.11 CONTENTS VII Y VII.5 LOCALIZATION 312 VII.6 GERM SOLVABILITY 313 VII.7 V-COHOMOLOGY AND LOCAL SOLVABILITY 315 VII. 8 THE APPROXIMATE POINCARE LEMMA 316 VII.9 ONE-SIDED SOLVABILITY 319 VII.10 LOCALIZATION NEAR A POINT AT THE BOUNDARY 321 VII. 11 ONE-SIDED APPROXIMATION 322 VII. 12 A MAYER-VIETORIS ARGUMENT 323 VII. 13 LOCAL SOLVABILITY VERSUS LOCAL INTEGRABILITY 328 NOTES 330 VIII LOCAL SOLVABILITY IN LOCALLY INTEGRABLE STRUCTURES 331 VIII. 1 LOCAL SOLVABILITY IN ESSENTIALLY REAL STRUCTURES 332 VIII.2 LOCAL SOLVABILITY IN THE ANALYTIC CATEGORY 332 VIII.3 ELLIPTIC STRUCTURES 333 VM.4 THE BOX OPERATOR ASSOCIATED WITH D 337 VIII.5 THE INTERSECTION NUMBER 340 VIII.6 THE INTERSECTION NUMBER UNDER CERTAIN GEOMETRICAL ASSUMPTIONS 343 VIII.7 A NECESSARY CONDITION FOR ONE-SIDED SOLVABILITY 346 VIII.8 THE SUFFICIENCY OF CONDITION ()* 348 VIII.9 PROOF OF PROPOSITION VIII.8.2 350 VIII. 10 SOLVABILITY FOR CORANK ONE ANALYTIC STRUCTURES 354 NOTES 357 EPILOGUE ( 361 1 THE SIMILARITY PRINCIPLE AND APPLICATIONS 361 2 MIZOHATA STRUCTURES 364 3 HYPOANALYTIC STRUCTURES 37 0 4 THE LOCAL MODEL FOR A HYPOANALYTIC MANIFOLD 371 5 THE SHEAF OF HYPERFUNCTION SOLUTIONS ON A HYPOANALYTIC MANIFOLD 372 APPENDIX A HARDY SPACE LEMMAS 374 A.I MULTIPLIERS IN H 374 A.2 COMMUTATORS 376 A3 CHANGE OF VARIABLES 378 BIBLIOGRAPHY 381 INDEX 390
adam_txt	AN INTRODUCTION TO INVOLUTIVE STRUCTURES SHIFERAW BERHANU TEMPLE UNIVERSITY PAULO D. CORDARO UNIVERSITY OF SAO PAULO JORGE HOUNIE FEDERAL UNIVERSITY OF SAO CARLOS CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE PAGE IX I LOCALLY INTEGRABLE STRUCTURES 1 1.1 COMPLEX VECTOR FIELDS - ' 1 1.2 THE ALGEBRAIC STRUCTURE OF X(L) 4 1.3 FORMALLY INTEGRABLE STRUCTURES 5 1.4 DIFFERENTIAL FORMS 7 1.5 THE FROBENIUS THEOREM . 11 1.6 ANALYTIC STRUCTURES , * 14 1.7 THE CHARACTERISTIC SET . . 15 1.8 SOME SPECIAL STRUCTURES 15 1.9 LOCALLY INTEGRABLE STRUCTURES .-., 19 1.10 LOCAL GENERATORS 21 1.11 LOCAL GENERATORS IN ANALYTIC STRUCTURES. . . 25 1.12 INTEGRABILITY OF COMPLEX AND ELLIPTIC STRUCTURES 26 1.13 ELLIPTIC STRUCTURES IN THE REAL PLANE 28 1.14 COMPATIBLE SUBMANIFOLDS -32 1.15 LOCALLY INTEGRABLE CR STRUCTURES - 36 1.16 A CR STRUCTURE THAT IS NOT LOCALLY INTEGRABLE 38 1.17 THE LEVI FORM ON A FORMALLY IHTEGRABLE STRUCTURE 42 APPENDIX: PROOF OF THE NEWLANDER-NIRENBERG THEOREM 47 NOTES 51 II THE BAOUENDI-TREVES APPROXIMATION FORMULA 52 II. 1 THE APPROXIMATION THEOREM 52 11.2 DISTRIBUTION SOLUTIONS 63 11.3 CONVERGENCE IN STANDARD FUNCTIONAL SPACES 69 11.4 APPLICATIONS 83 N O T E S * '* *** * * * * ' * - ' 99 VI CONTENTS Y III SUSSMANN'S ORBITS AND UNIQUE CONTINUATION 101 111.1 SUSSMANN'S ORBITS 101 111.2 PROPAGATION OF SUPPORT AND GLOBAL UNIQUE CONTINUATION 108 111.3 THE STRONG UNIQUENESS PROPERTY FOR LOCALLY INTEGRABLE SOLUTIONS 120 111.4 PROOF OF THEOREM III.3.15 126 111.5 UNIQUENESS FOR APPROXIMATE SOLUTIONS 132 111.6 REAL-ANALYTIC STRUCTURES IN THE PLANE 140 111.7 FURTHER APPLICATIONS OF SUSSMANN'S ORBITS 146 NOTES 147 IV LOCAL SOLVABILITY OF VECTOR FIELDS IV. 1 PLANAR VECTOR FIELDS ''' IV.2 SOLVABILITY IN C IV.3 VECTOR FIELDS IN SEVERAL VARIABLES , . . ; IV.4 NECESSARY CONDITIONS FOR LOCAL SOLVABILITY * ' NOTES * * ; * ' ' - * * , * * : . * . . . * . . . ' * : V THE FBI TRANSFORM AND SOME'APPLICATIONS V. 1 CERTAIN SUBMANIFOLDS OF HYPOANALYTIC MANIFOLDS V.2 MICROLOCAL ANALYTICITY AND THE FBI TRANSFORM V.3 MICROLOCAL SMOOTHNESS V.4 MICROLOCAL HYPOANALYTICITY AND THE FBI TRANSFORM V.5 APPLICATION OF THE FBI TRANSFORM TO THE C" 30 WAVE FRONT SET OF SOLUTIONS OF NONLINEAR PDES V.6 APPLICATIONS TO EDGE-OF-THE-WEDGE THEORY V.7 APPLICATION TO THE F. AND M.'RIESZ THEOREM N O T E S ' ' '* : ' ' " '' " * * . ' ' * * VI SOME BOUNDARY PROPERTIES OF SOLUTIONS .,. , 271 VI. 1 EXISTENCE OF A BOUNDARY VALUE , , . . , * 271 VI.2 POINTWISE, CONVERGENCE TO THE BOUNDARY VALUE . , ; 281 VI.3 ONE-SIDED LOCAL SOLVABILITY IN THE PLANE , .-. . 286 VI.4 THE//". PROPERTY FOR VECTOR FIELDS . . . 289 NOTES 307 VII THE DIFFERENTIAL COMPLEX ASSOCIATED WITH A FORMALLY F , INTEGRABLE STRUCTURE .,,, , 308 . VII.L THE EXTERIOR DERIVATIVE . . ., ; : . . ,308 VII.2 THE LOCAL REPRESENTATION .OF THE EXTERIOR, DERIVATIVE -. . ,309 VII.3 THE POINCARE LEMMA ., , , , - 311 VII.4 THE DIFFERENTIAL COMPLEX ASSOCIATED WITH A FORMALLY INTEGRABLE STRUCTURE 3.11 CONTENTS VII Y VII.5 LOCALIZATION 312 VII.6 GERM SOLVABILITY 313 VII.7 V-COHOMOLOGY AND LOCAL SOLVABILITY 315 VII. 8 THE APPROXIMATE POINCARE LEMMA 316 VII.9 ONE-SIDED SOLVABILITY 319 VII.10 LOCALIZATION NEAR A POINT AT THE BOUNDARY 321 VII. 11 ONE-SIDED APPROXIMATION 322 VII. 12 A MAYER-VIETORIS ARGUMENT 323 VII. 13 LOCAL SOLVABILITY VERSUS LOCAL INTEGRABILITY 328 NOTES 330 VIII LOCAL SOLVABILITY IN LOCALLY INTEGRABLE STRUCTURES 331 VIII. 1 LOCAL SOLVABILITY IN ESSENTIALLY REAL STRUCTURES 332 VIII.2 LOCAL SOLVABILITY IN THE ANALYTIC CATEGORY 332 VIII.3 ELLIPTIC STRUCTURES 333 VM.4 THE BOX OPERATOR ASSOCIATED WITH D 337 VIII.5 THE INTERSECTION NUMBER 340 VIII.6 THE INTERSECTION NUMBER UNDER CERTAIN GEOMETRICAL ASSUMPTIONS 343 VIII.7 A NECESSARY CONDITION FOR ONE-SIDED SOLVABILITY 346 VIII.8 THE SUFFICIENCY OF CONDITION ()* 348 VIII.9 PROOF OF PROPOSITION VIII.8.2 350 VIII. 10 SOLVABILITY FOR CORANK ONE ANALYTIC STRUCTURES 354 NOTES 357 EPILOGUE ( 361 1 THE SIMILARITY PRINCIPLE AND APPLICATIONS 361 2 MIZOHATA STRUCTURES 364 3 HYPOANALYTIC STRUCTURES 37 0 4 THE LOCAL MODEL FOR A HYPOANALYTIC MANIFOLD 371 5 THE SHEAF OF HYPERFUNCTION SOLUTIONS ON A HYPOANALYTIC MANIFOLD 372 APPENDIX A HARDY SPACE LEMMAS 374 A.I MULTIPLIERS IN H' 374 A.2 COMMUTATORS 376 A3 CHANGE OF VARIABLES 378 BIBLIOGRAPHY 381 INDEX 390
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spelling	Berhanu, Shiferaw Verfasser aut An introduction to involutive structures Shiferaw Berhanu ; Paulo D. Cordaro ; Jorge Hounie 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2008 XII, 392 S. txt rdacontent n rdamedia nc rdacarrier New mathematical monographs 6 Literaturverz. S. 381 - 389 Approximation theory Bivectors Differential equations, Partial Vector fields Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Vektorfeld (DE-588)4139571-2 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Vektorfeld (DE-588)4139571-2 s Approximationstheorie (DE-588)4120913-8 s DE-604 Cordaro, Paulo D. Verfasser aut Hounie, Jorge Verfasser aut New mathematical monographs 6 (DE-604)BV035420183 6 http://www.gbv.de/dms/goettingen/547670516.pdf lizenzfrei Inhaltsverzeichnis GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016526115&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Berhanu, Shiferaw Cordaro, Paulo D. Hounie, Jorge An introduction to involutive structures New mathematical monographs Approximation theory Bivectors Differential equations, Partial Vector fields Partielle Differentialgleichung (DE-588)4044779-0 gnd Approximationstheorie (DE-588)4120913-8 gnd Vektorfeld (DE-588)4139571-2 gnd
subject_GND	(DE-588)4044779-0 (DE-588)4120913-8 (DE-588)4139571-2
title	An introduction to involutive structures
title_auth	An introduction to involutive structures
title_exact_search	An introduction to involutive structures
title_exact_search_txtP	An introduction to involutive structures
title_full	An introduction to involutive structures Shiferaw Berhanu ; Paulo D. Cordaro ; Jorge Hounie
title_fullStr	An introduction to involutive structures Shiferaw Berhanu ; Paulo D. Cordaro ; Jorge Hounie
title_full_unstemmed	An introduction to involutive structures Shiferaw Berhanu ; Paulo D. Cordaro ; Jorge Hounie
title_short	An introduction to involutive structures
title_sort	an introduction to involutive structures
topic	Approximation theory Bivectors Differential equations, Partial Vector fields Partielle Differentialgleichung (DE-588)4044779-0 gnd Approximationstheorie (DE-588)4120913-8 gnd Vektorfeld (DE-588)4139571-2 gnd
topic_facet	Approximation theory Bivectors Differential equations, Partial Vector fields Partielle Differentialgleichung Approximationstheorie Vektorfeld
url	http://www.gbv.de/dms/goettingen/547670516.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016526115&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV035420183
work_keys_str_mv	AT berhanushiferaw anintroductiontoinvolutivestructures AT cordaropaulod anintroductiontoinvolutivestructures AT houniejorge anintroductiontoinvolutivestructures

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