Partial differential equations: 2 Qualitative studies of linear equations
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [und andere]
Springer
1997
|
| Edition: | Corr. 2. printing |
| Series: | Applied mathematical sciences
116 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 528 S. graph. Darst. |
| ISBN: | 0387946519 |
Staff View
MARC
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| 100 | 1 | |a Taylor, Michael Eugene |d 1946- |e Verfasser |0 (DE-588)123980119 |4 aut | |
| 245 | 1 | 0 | |a Partial differential equations |n 2 |p Qualitative studies of linear equations |c Michael E. Taylor |
| 250 | |a Corr. 2. printing | ||
| 264 | 1 | |a New York [und andere] |b Springer |c 1997 | |
| 300 | |a XXI, 528 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Applied mathematical sciences |v 116 | |
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Record in the Search Index
| _version_ | 1805066157073367040 |
|---|---|
| adam_text |
Contents
Contents
of Volumes I and III
xi
Introduction
xiii
7
Pseudodifferential Operators
1
Introduction
1
1
The Fourier integral representation and symbol classes
2
2
Schwartz kernels of pseudodifferential operators
5
3
Adjoints
and products
9
4
Elliptic operators and parametrices
14
5
¿^-estimates
16
6
Garding's inequality
19
7
Hyperbolic evolution equations
21
8
Egorov's theorem
24
9
Microlocal
regularity
26
10
Operators on manifolds
30
11
The method of layer potentials
33
12
Parametrix for regular elliptic boundary problems
43
13
Parametrix for the heat equation
50
14
The Weyl calculus
60
References
70
8
Spectra] Theory
74
Introduction
74
1
The spectral theorem
75
2
Self-adjoint differential operators
82
3
Heat asymptotics and eigenvalue asymptotics
88
4
The Laplace operator on
5" 94
5
The Laplace operator on hyperbolic space
103
6
The harmonic oscillator
105
7
The quantum Coulomb problem
113
8
The Laplace operator on cones
126
References
142
viii Contents
9
Scattering by Obstacles
145
Introduction
145
1
The scattering problem
147
2
Eigenfunction expansions
155
3
The scattering operator
161
4
Connections with the wave equation
165
5
Wave operators
172
6
Translation representations and the Lax-Phillips semigroup
Z(t)
177
7
Integral equations and scattering poles
184
8
Trace formulas; the scattering phase
197
9
Scattering by a sphere
203
10
Inverse problems I
211
11
Inverse problems II
217
12
Scattering by rough obstacles
227
A Lidskii's trace theorem
235
References
237
10
Dirac Operators and Index Theory
241
Introduction
241
1
Operators of Dirac type
242
2
Clifford algebras
248
3
Spinors
253
4
Weitzenbock formulas
258
5
Index of Dirac operators
264
6
Proof of the local index formula
267
7
The Chern-Gauss-Bonnet theorem
273
8
Spur manifolds
277
9
The Riemann-Roch theorem
281
10
Direct attack in 2-D
292
References
298
11
Brownian Motion and Potential Theory
301
Introduction
301
1
Brownian motion and Wiener measure
303
2
The Feynman-Kac formula
310
3
The Dirichlet problem and diffusion on domains with
boundary
314
4
Martingales, stopping times, and the strong Markov property
322
5
First exit time and the
Poisson
integral
331
6
Newtonian capacity
335
7
Stochastic integrals
349
8
Stochastic integrals, II
358
Contents ix
9
Stochastic differential equations
364
10
Application to equations of diffusion
371
A The Trotter product formula
380
References
386
12
The d-Neumann Problem
389
Introduction
389
A Elliptic complexes
391
1
The 3-complex
396
2
Morrey's inequality, the
Levi
form, and strong pseudoconvexity
399
3
The \ -estimate and some consequences
402
4
Higher-order subelliptic estimates
406
5
Regularity via elliptic regularization
409
6
The Hodge decomposition and the 9-equation
412
7
The Bergman projection and Toeplitz operators
415
8
The 9-Neumann problem on
(0,
<?)-forms
421
9
Reduction to pseudodifferential equations on the boundary
429
10
The 3-equation on complex manifolds and almost complex
manifolds
440
В
Complements on the
Levi
form
449
С
The Neumann operator for the Dirichlet problem
453
References
456
С
Connections and Curvature
460
Introduction
460
1
Covariant derivatives and curvature on general vector bundles
461
2
Second covariant derivatives and covariant-exterior derivatives
466
3
The curvature tensor of a Riemannian manifold
468
4
Geometry of submanifolds and subbundles
479
5
The Gauss-Bonnet theorem for surfaces
492
6
The principal bundle picture
502
7
The Chern-Weil construction
509
8
The Chem-Gauss-Bonnet theorem
514
References
522
Index
525 |
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| author | Taylor, Michael Eugene 1946- |
| author_GND | (DE-588)123980119 |
| author_facet | Taylor, Michael Eugene 1946- |
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| author_sort | Taylor, Michael Eugene 1946- |
| author_variant | m e t me met |
| building | Verbundindex |
| bvnumber | BV012271909 |
| classification_rvk | SK 540 |
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| discipline | Mathematik |
| edition | Corr. 2. printing |
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| id | DE-604.BV012271909 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T03:13:52Z |
| institution | BVB |
| isbn | 0387946519 |
| language | English |
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| oclc_num | 174888127 |
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| physical | XXI, 528 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Taylor, Michael Eugene 1946- Verfasser (DE-588)123980119 aut Partial differential equations 2 Qualitative studies of linear equations Michael E. Taylor Corr. 2. printing New York [und andere] Springer 1997 XXI, 528 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 116 Applied mathematical sciences (DE-604)BV010899159 2 Applied mathematical sciences 116 (DE-604)BV000005274 116 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008317539&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| 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 |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008317539&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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