The analysis of linear partial differential operators: 1 Distribution theory and Fourier analysis
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer
1990
|
| Ausgabe: | Reprint of the 2. ed. 1990 |
| Schriftenreihe: | Classics in mathematics
Die Grundlehren der mathematischen Wissenschaften |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [419] - 436. - Orig. publ. as Vol. 256 in the series: Grundlehren der mathematischen Wissenschaften |
| Beschreibung: | XI, 440 S. graph. Darst. |
| ISBN: | 354052343X 038752343X |
Internformat
MARC
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| 245 | 1 | 0 | |a The analysis of linear partial differential operators |n 1 |p Distribution theory and Fourier analysis |c Lars Hörmander |
| 250 | |a Reprint of the 2. ed. 1990 | ||
| 264 | 1 | |a Berlin |b Springer |c 1990 | |
| 300 | |a XI, 440 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Classics in mathematics | |
| 490 | 0 | |a Die Grundlehren der mathematischen Wissenschaften | |
| 500 | |a Literaturverz. S. [419] - 436. - Orig. publ. as Vol. 256 in the series: Grundlehren der mathematischen Wissenschaften | ||
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Datensatz im Suchindex
| _version_ | 1804140693240676352 |
|---|---|
| adam_text | Contents
Introduction
....................... 1
Chapter I. Test Functions
................. 5
Summary
....................... 5
1.1.
A review of Differential Calculus
........... 5
1.2.
Existence of Test Functions
............. 14
1.3.
Convolution
.................... 16
1.4.
Cutoff Functions and Partitions of Unity
....... 25
Notes
......................... 31
Chapter II. Definition and Basic Properties of Distributions
. . 33
Summary
....................... 33
2.1.
Basic Definitions
.................. 33
2.2.
Localization
.................... 41
2.3.
Distributions with Compact Support
......... 44
Notes
......................... 52
Chapter III. Differentiation and Multiplication by Functions
. . 54
Summary
....................... 54
3.1.
Definition and Examples
.............. 54
3.2.
Homogeneous Distributions
............. 68
3.3.
Some Fundamental Solutions
............ 79
3.4.
Evaluation of Some Integrals
............. 84
Notes
......................... 86
Chapter IV. Convolution
................. 87
Summary
....................... 87
4.1.
Convolution with a Smooth Function
......... 88
4.2.
Convolution of Distributions
............. 100
4.3.
The Theorem of Supports
.............. 105
4.4.
The Role of Fundamental Solutions
.......... 109
X
Contents
4.5.
Basic L Estimâtes
for Convolutions
..........116
Notes
.........................
I24
Chapter V. Distributions in Product Spaces
.........126
Summary
....................... 126
5.1.
Tensor Products
.................. 126
5.2.
The Kernel Theorem
................ 128
Notes
......................... 132
Chapter VI. Composition with Smooth Maps
.........133
Summary
....................... 133
6.1.
Definitions
..................... 133
6.2.
Some Fundamental Solutions
............ 137
6.3.
Distributions on a Manifold
............. 142
6.4.
The Tangent and Cotangent Bundles
......... 146
Notes
......................... 156
Chapter
VII.
The Fourier Transformation
..........158
Summary
....................... 158
7.1.
The Fourier Transformation in
У
and in
ЅЃ
...... 159
7.2.
Poisson s Summation Formula and Periodic Distributions
177
7.3.
The Fourier-Laplace Transformation in
ď
....... 181
7.4.
More General Fourier-Laplace Transforms
....... 191
7.5.
The
Malgrange
Preparation Theorem
......... 195
7.6.
Fourier Transforms of Gaussian Functions
....... 205
7.7.
The Method of Stationary Phase
........... 215
7.8.
Oscillatory Integrals
................ 236
7.9.
ff(s), I? and Holder Estimates
............ 240
Notes
......................... 248
Chapter
VIII.
Spectral Analysis of Singularities
........251
Summary
....................... 251
8.1.
The Wave Front Set
................252
8.2.
A Review of Operations with Distributions
......261
8.3.
The Wave Front Set of Solutions of Partial Differential
Equations
......................271
8.4.
The Wave Front Set with Respect to CL
........280
8.5.
Rules of Computation for WFL
............296
8.6.
WFL for Solutions of Partial Differential Equations
... 305
8.7.
Microhyperbolicity
.................317
Notes
.........................322
Contents
XI
Chapter IX. Hyperfunctions
................ 325
Summary
....................... 325
9.1.
Analytic Functionals
................ 326
9.2.
General Hyperfunctions
............... 335
9.3.
The Analytic Wave Front Set of a Hyperfunction
.... 338
9.4.
The Analytic Cauchy Problem
............ 346
9.5.
Hyperfunction Solutions of Partial Differential Equations
353
9.6.
The Analytic Wave Front Set and the Support
..... 358
Notes
......................... 368
Exercises
........................ 371
Answers and Hints to All the Exercises
............ 394
Bibliography
....................... 419
Index
.......................... 437
Index of Notation
..................... 439
|
| any_adam_object | 1 |
| author | Hörmander, Lars 1931-2012 |
| author_GND | (DE-588)105823449 |
| author_facet | Hörmander, Lars 1931-2012 |
| author_role | aut |
| author_sort | Hörmander, Lars 1931-2012 |
| author_variant | l h lh |
| building | Verbundindex |
| bvnumber | BV035766217 |
| classification_rvk | SK 620 |
| ctrlnum | (OCoLC)311387065 (DE-599)BVBBV035766217 |
| dewey-full | 515.7242 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7242 515.353 |
| dewey-search | 515.7242 515.353 |
| dewey-sort | 3515.7242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Reprint of the 2. ed. 1990 |
| format | Book |
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| id | DE-604.BV035766217 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:02Z |
| institution | BVB |
| isbn | 354052343X 038752343X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018626000 |
| oclc_num | 311387065 |
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| owner | DE-355 DE-BY-UBR DE-20 |
| owner_facet | DE-355 DE-BY-UBR DE-20 |
| physical | XI, 440 S. graph. Darst. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Springer |
| record_format | marc |
| series2 | Classics in mathematics Die Grundlehren der mathematischen Wissenschaften |
| spelling | Hörmander, Lars 1931-2012 Verfasser (DE-588)105823449 aut The analysis of linear partial differential operators 1 Distribution theory and Fourier analysis Lars Hörmander Reprint of the 2. ed. 1990 Berlin Springer 1990 XI, 440 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Classics in mathematics Die Grundlehren der mathematischen Wissenschaften Literaturverz. S. [419] - 436. - Orig. publ. as Vol. 256 in the series: Grundlehren der mathematischen Wissenschaften (DE-604)BV000157227 1 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018626000&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hörmander, Lars 1931-2012 The analysis of linear partial differential operators |
| title | The analysis of linear partial differential operators |
| title_auth | The analysis of linear partial differential operators |
| title_exact_search | The analysis of linear partial differential operators |
| title_full | The analysis of linear partial differential operators 1 Distribution theory and Fourier analysis Lars Hörmander |
| title_fullStr | The analysis of linear partial differential operators 1 Distribution theory and Fourier analysis Lars Hörmander |
| title_full_unstemmed | The analysis of linear partial differential operators 1 Distribution theory and Fourier analysis Lars Hörmander |
| title_short | The analysis of linear partial differential operators |
| title_sort | the analysis of linear partial differential operators distribution theory and fourier analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018626000&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000157227 |
| work_keys_str_mv | AT hormanderlars theanalysisoflinearpartialdifferentialoperators1 |