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Partial differential equations: 2 Qualitative studies of linear equations

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Bibliographic Details
Main Author:	Taylor, Michael Eugene 1946- (Author)
Format:	Book
Language:	English
Published:	New York [und andere] Springer 2011
Edition:	2. ed.
Series:	Applied mathematical sciences 116
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020537594&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	XXII, 614 S. graph. Darst.
ISBN:	9781441970510 9781461427421

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MARC


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adam_text	Contents Contents of Volumes I and ΠΙ ................................................. χι Preface ............................................................................ xiii 7 Pseudodifferential Operators ............................................. 1 1 The Founer integral representation and symbol classes ............. 2 2 Schwartz kernels of pseudodifferential operators .................... 5 3 Adjoints and products ................................................. 10 4 Elliptic operators and paramétrées ................................... 15 5 L2-esnmates ........................................................... 18 6 Gârdmg s inequality ................................................... 22 7 Hyperbolic evolution equations ....................................... 23 8 Egorov s theorem ...................................................... 26 9 Microlocal regularity .................................................. 29 10 Operators on manifolds ............................................... 33 11 The method of layer potentials ....................................... 36 12 Paraxnetrix for regular elliptic boundary problems .................. 47 13 Parametrix for the heat equation ...................................... 56 14 The Weyl calculus ......................................................... 67 15 Operators of iutmoooic oscillator type .................................... 80 References .................................................................... SB 8 ЅцшѕхѕаТШжу«.. ............................................................. 91 1 The spectral theorem ..........____..........___..___............... 92 2 Sełf-adjoint differential operatore ....... , ......___.................. ÌOO 3 Нем asymptote ахкІ eigenvalue asymptote ....................... Í06 4 The Laplaceoperator ой S ..........................................113 5 The Laplace operator on hypedxwUsc space ........................... 123 6 The harmonic oscil) ator .................................................126 7 The quantum Coulomb problem .......................................135 8 The Laplace operator on cones ........___,.........................149 References ..................—....................................... 17 ! 9 Scattala« by Obstacles .................................................... 175 1 The scattering problem ................................................ 1 77 2 EigeafiinctioQ expansions .............................................186 3 The scattering operator..., ...........,................................192 viii Contents 4 Connections wiih the wave equation ................................. 197 5 Wave operators ........................................................205 6 Translation representations and Lbe Lax-Phihips semigroup 7,(t) .........................................................211 7 Integra] equations and scattering poles ...............................218 8 Trace formulas; the scattering phase .................................232 9 Scattering by a sphere .................................................239 10 I riverse problems I .....................................................248 11 Inverse problems II ....................................................254 12 Scattering by rough obstacles .........................................266 A Lidsku s trace theorem ................................................275 References .............................................................277 10 Dirac Operators and Index Theory ......................................281 1 Operators of Dirac type ...............................................283 2 Clifford algebras .......................................................289 3 Spinors .................................................................294 4 Weitzenbock formulas ................................................300 5 Index of Dirac operators ...............................................306 6 Proof of the local index formula ......................................309 7 The Chern-Gaiiss -Bonnet theorem ..................................3 1.6 8 Spmc manifolds .......................................................320 9 The Riemann-Roch theorem .........................................325 10 Direct attack in 2-D ...................................................338 11 Index of operators of harmonic oscillator type .......................345 References .............................................................358 11 Brownian Motion and Potential Theory ................................361 1 Brownian motion and Wiener measure ...............................363 2 The Feynman-Kac formula ...........................................370 3 The DmchJet problem and diffusion on domains with boundary ... 375 4 Martingales, stopping times, and the strong Markov property ......384 5 First exit time and the Poisson i n t egra! ...............................394 6 Newtonian capacity ...................................................398 7 Stochastic integrals ....................................................412 8 Stochastic integrals, II .................................................423 9 Stochastic differential equations ...................................... 430 10 Application to equations of diffusion .................................437 A The Trotter product formula ..........................................448 References .............................................................454 12 The 3 -Neumann Problem .................................................457 A Elliptic complexes .....................................................460 1 The З-сотріех .........................................................465 2 Money s inequality, the Levi form, and strong pseudoconvexity ... 469 3 The \| -esumate and some consequences .............................472 С ο η te піч їх 4 Higher-order subeljiplic esi ι maies ..............................4 76 5 Regularity via elliptic regulanzaiion ........................... 480 6 The Hodge decomposition and the S-cquation .............. 483 7 The Bergman projection and ! oephi/ operators ................487 8 The Э -Neumann problem on (0. q )■■ forms ..................... 494 9 Reduction to pseudodiffercnual equations on the, boundary ... . 503 10 The д equation on complex mnmioids and almost complex manifolds ....... ........................ 5 ! 6 В Complements on the Levi loi m ..................... 5/7 С The Neumann operator tor ine Dinchlei. problem ..........531 References ................. ..........................535 С Connections and Curvature 539 1 Covanani derivatives and curvature on generai vecioi bundles .. 5-10 2 Second covariant derivatives and covenant exterior deriva: ivcs . . 546 3 The curvature tensor of a Ricmanmar: manifold ............. 548 4 Geometry of submanifolds ar.d subbund .es ............ . 360 5 The Gauss-Bonnet theorem :o; surfaces ......... . ^74 6 The principal bundle pici;. re ...............586 7 The Chem-Weil construcion . .................. 59·! 8 The Chern-Gauss-Bonne; ι lieoi cm .................. 598 References ................................ . . 608 Index .................................. .....................611
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series	Applied mathematical sciences
series2	Applied mathematical sciences
spellingShingle	Taylor, Michael Eugene 1946- Partial differential equations Applied mathematical sciences
title	Partial differential equations
title_auth	Partial differential equations
title_exact_search	Partial differential equations
title_full	Partial differential equations 2 Qualitative studies of linear equations Michael E. Taylor
title_fullStr	Partial differential equations 2 Qualitative studies of linear equations Michael E. Taylor
title_full_unstemmed	Partial differential equations 2 Qualitative studies of linear equations Michael E. Taylor
title_short	Partial differential equations
title_sort	partial differential equations qualitative studies of linear equations
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