Linear partial differential operators:
Gespeichert in:
| Späterer Titel: | Hörmander, Lars The analysis of linear partial differential operators |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1976
|
| Ausgabe: | 4. print. |
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften
116 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 285 S. graph. Darst. |
| ISBN: | 3540045007 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV006240298 | ||
| 003 | DE-604 | ||
| 005 | 20211123 | ||
| 007 | t | ||
| 008 | 930210s1976 d||| |||| 00||| eng d | ||
| 020 | |a 3540045007 |9 3-540-04500-7 | ||
| 035 | |a (OCoLC)185672354 | ||
| 035 | |a (DE-599)BVBBV006240298 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-739 |a DE-703 |a DE-20 |a DE-355 |a DE-1046 |a DE-824 |a DE-188 |a DE-83 | ||
| 084 | |a SK 620 |0 (DE-625)143249: |2 rvk | ||
| 084 | |a 35-01 |2 msc | ||
| 084 | |a 47F05 |2 msc | ||
| 100 | 1 | |a Hörmander, Lars |d 1931-2012 |e Verfasser |0 (DE-588)105823449 |4 aut | |
| 245 | 1 | 0 | |a Linear partial differential operators |c Lars Hörmander |
| 250 | |a 4. print. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1976 | |
| 300 | |a VII, 285 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften |v 116 | |
| 650 | 4 | |a General theory of first order linear PDE | |
| 650 | 4 | |a General theory of linear higher-order PDE | |
| 650 | 0 | 7 | |a Lineare partielle Differentialgleichung |0 (DE-588)4167708-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Partieller Differentialoperator |0 (DE-588)4173439-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Linearer partieller Differentialoperator |0 (DE-588)4167722-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differentialoperator |0 (DE-588)4012251-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Distribution |g Funktionalanalysis |0 (DE-588)4070505-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Linearer Differentialoperator |0 (DE-588)4167717-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare partielle Differentialgleichung |0 (DE-588)4167708-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Linearer partieller Differentialoperator |0 (DE-588)4167722-5 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Partieller Differentialoperator |0 (DE-588)4173439-7 |D s |
| 689 | 2 | |5 DE-604 | |
| 689 | 3 | 0 | |a Linearer Differentialoperator |0 (DE-588)4167717-1 |D s |
| 689 | 3 | |5 DE-604 | |
| 689 | 4 | 0 | |a Differentialoperator |0 (DE-588)4012251-7 |D s |
| 689 | 4 | |5 DE-604 | |
| 689 | 5 | 0 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |D s |
| 689 | 5 | |5 DE-604 | |
| 689 | 6 | 0 | |a Distribution |g Funktionalanalysis |0 (DE-588)4070505-5 |D s |
| 689 | 6 | |5 DE-604 | |
| 785 | 0 | 0 | |i Später u.d.T. |a Hörmander, Lars |t The analysis of linear partial differential operators |w (DE-604)BV027260502 |
| 830 | 0 | |a Grundlehren der mathematischen Wissenschaften |v 116 |w (DE-604)BV000000395 |9 116 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003940558&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-003940558 | ||
Datensatz im Suchindex
| _version_ | 1804120455218462720 |
|---|---|
| adam_text | Contents
Part I: Functional analysis
Chapter I. Distribution theory 1
1.0. Introduction 1
1.1. Weak derivatives 1
1.2. Test functions 2
1.3. Definitions and basic properties of distributions 4
1.4. Differentiation of distributions and multiplication by functions ... 7
1.5. Distributions with compact support 10
1.6. Convolution of distributions 13
1.7. Fourier transforms of distributions 17
1.8. Distributions on a manifold 25
Chapter II. Some special spaces of distributions 33
2.0. Introduction 33
2.1. Temperate weight functions 34
2.2. The spaces mpk 36
2.3. The spaces 3J~k 42
2.4. The spaces Jt7U) 45
2.5. The spaces ¦* „.„ 51
2.6. The spaces Mf ^{Q) when Q is a manifold 56
Part II: Differential operators with constant coefficients
Chapter III. Existence and approximation of solutions of differential equations 63
3.0. Introduction 63
3.1. Existence of fundamental solutions 64
3.2. The equation P(£ )«=/ when /£ ? 69
3.3. Comparison of differential operators 71
3.4. Approximation of solutions of homogeneous differential equations . . 76
3.5. The equation P (D) u =f when / is in a local space C B r ....•¦• 80
3.6. The equation P(D)u = f when f^Q 83
3.7. The geometric meaning of P-convexity and strong P-convexity ... 89
3.8. Systems of differential operators 94
Chapter IV. Interior regularity of solutions of differential equations 96
4.0. Introduction 96
4.1. Hypoelliptic operators 97
4.2. Partially hypoelliptic operators 104
4.3. Partial hypoellipticity at the boundary 107
4.4. Estimates for derivatives of high order 108
Chapter V. The Cauchy problem (constant coefficients) 114
5.0. Introduction 114
5.1. The classical existence theory for analytic data 116
5.2. The non-uniqueness of the characteristic Cauchy problem 120
Contents VII
5.3. Holmgrens uniqueness theorem 123
5.4. The necessity of hyperbolicity for the existence of solutions to the non-
characteristic Cauchy problem 130
5.5. Algebraic properties of hyperbolic polynomials 132
5.6. The Cauchy problem for a hyperbolic equation 137
5.7. A global uniqueness theorem 142
5.8. The characteristic Cauchy problem 151
Part III: Differential operators with variable coefficients
Chapter VI. Differential equations which have no solutions 156
6.0. Introduction 156
6.1. Conditions for non-existence 156
6.2. Some properties of the range 166
Chapter VII. Differential operators of constant strength 170
7.0. Introduction 170
7.1. Definitions and basic properties 170
7.2. Existence theorems when the coefficients are merely continuous . . . 172
7.3. Existence theorems when the coefficients are in C°° 173
7.4. Hypoellipticity 176
7.5. The analyticity of the solutions of elliptic equations 177
Chapter VIII. Differential operators with simple characteristics 180
8.0. Introduction 180
8.1. Necessary conditions for the main estimates 181
8.2. Differential quadratic forms 187
8.3. Estimates for elliptic operators 190
8.4. Estimates for operators with real coefficients 193
8.5. Estimates for principally normal operators 199
8.6. Pseudo-convexity 202
8.7. Estimates, existence and approximation theorems in Jf,,, 207
8.8. The unique continuation of singularities 216
8.9. The uniqueness of the Cauchy problem 224
Chapter IX. The Cauchy problem (variable coefficients) 230
9.0. Introduction 230
9.1. Preliminary lemmas 230
9.2. The basic i2 estimate 234
9.3. Existence theory for the Cauchy problem 237
Chapter X. Elliptic boundary problems 242
10.0. Introduction 242
10.1. Definition of elliptic boundary problems 243
10.2. Preliminaries concerning ordinary differential operators 246
10.3. Construction of a parametrix 248
10.4. Local theory of elliptic boundary problems 254
10.5. Elliptic boundary problems in a compact manifold with boundary . . 258
10.6. Various extensions and remarks 267
Appendix. Some algebraic lemmas 275
Bibliography 280
Index 286
Indexofnotations 287
|
| 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 | BV006240298 |
| classification_rvk | SK 620 |
| ctrlnum | (OCoLC)185672354 (DE-599)BVBBV006240298 |
| discipline | Mathematik |
| edition | 4. print. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02801nam a2200625 cb4500</leader><controlfield tag="001">BV006240298</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20211123 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">930210s1976 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540045007</subfield><subfield code="9">3-540-04500-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)185672354</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV006240298</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-739</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-1046</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 620</subfield><subfield code="0">(DE-625)143249:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">35-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">47F05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hörmander, Lars</subfield><subfield code="d">1931-2012</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)105823449</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Linear partial differential operators</subfield><subfield code="c">Lars Hörmander</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">4. print.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1976</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VII, 285 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Grundlehren der mathematischen Wissenschaften</subfield><subfield code="v">116</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">General theory of first order linear PDE</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">General theory of linear higher-order PDE</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lineare partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4167708-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Partieller Differentialoperator</subfield><subfield code="0">(DE-588)4173439-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Linearer partieller Differentialoperator</subfield><subfield code="0">(DE-588)4167722-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4044779-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Differentialoperator</subfield><subfield code="0">(DE-588)4012251-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Distribution</subfield><subfield code="g">Funktionalanalysis</subfield><subfield code="0">(DE-588)4070505-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Linearer Differentialoperator</subfield><subfield code="0">(DE-588)4167717-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Lineare partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4167708-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Linearer partieller Differentialoperator</subfield><subfield code="0">(DE-588)4167722-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Partieller Differentialoperator</subfield><subfield code="0">(DE-588)4173439-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="3" ind2="0"><subfield code="a">Linearer Differentialoperator</subfield><subfield code="0">(DE-588)4167717-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="4" ind2="0"><subfield code="a">Differentialoperator</subfield><subfield code="0">(DE-588)4012251-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="4" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="5" ind2="0"><subfield code="a">Partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4044779-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="5" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="6" ind2="0"><subfield code="a">Distribution</subfield><subfield code="g">Funktionalanalysis</subfield><subfield code="0">(DE-588)4070505-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="6" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="785" ind1="0" ind2="0"><subfield code="i">Später u.d.T.</subfield><subfield code="a">Hörmander, Lars</subfield><subfield code="t">The analysis of linear partial differential operators</subfield><subfield code="w">(DE-604)BV027260502</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Grundlehren der mathematischen Wissenschaften</subfield><subfield code="v">116</subfield><subfield code="w">(DE-604)BV000000395</subfield><subfield code="9">116</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003940558&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-003940558</subfield></datafield></record></collection> |
| id | DE-604.BV006240298 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:42:21Z |
| institution | BVB |
| isbn | 3540045007 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003940558 |
| oclc_num | 185672354 |
| open_access_boolean | |
| owner | DE-739 DE-703 DE-20 DE-355 DE-BY-UBR DE-1046 DE-824 DE-188 DE-83 |
| owner_facet | DE-739 DE-703 DE-20 DE-355 DE-BY-UBR DE-1046 DE-824 DE-188 DE-83 |
| physical | VII, 285 S. graph. Darst. |
| publishDate | 1976 |
| publishDateSearch | 1976 |
| publishDateSort | 1976 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Hörmander, Lars 1931-2012 Verfasser (DE-588)105823449 aut Linear partial differential operators Lars Hörmander 4. print. Berlin [u.a.] Springer 1976 VII, 285 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 116 General theory of first order linear PDE General theory of linear higher-order PDE Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd rswk-swf Partieller Differentialoperator (DE-588)4173439-7 gnd rswk-swf Linearer partieller Differentialoperator (DE-588)4167722-5 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Differentialoperator (DE-588)4012251-7 gnd rswk-swf Distribution Funktionalanalysis (DE-588)4070505-5 gnd rswk-swf Linearer Differentialoperator (DE-588)4167717-1 gnd rswk-swf Lineare partielle Differentialgleichung (DE-588)4167708-0 s DE-604 Linearer partieller Differentialoperator (DE-588)4167722-5 s Partieller Differentialoperator (DE-588)4173439-7 s Linearer Differentialoperator (DE-588)4167717-1 s Differentialoperator (DE-588)4012251-7 s Partielle Differentialgleichung (DE-588)4044779-0 s Distribution Funktionalanalysis (DE-588)4070505-5 s Später u.d.T. Hörmander, Lars The analysis of linear partial differential operators (DE-604)BV027260502 Grundlehren der mathematischen Wissenschaften 116 (DE-604)BV000000395 116 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003940558&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hörmander, Lars 1931-2012 Linear partial differential operators Grundlehren der mathematischen Wissenschaften General theory of first order linear PDE General theory of linear higher-order PDE Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Partieller Differentialoperator (DE-588)4173439-7 gnd Linearer partieller Differentialoperator (DE-588)4167722-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Differentialoperator (DE-588)4012251-7 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd Linearer Differentialoperator (DE-588)4167717-1 gnd |
| subject_GND | (DE-588)4167708-0 (DE-588)4173439-7 (DE-588)4167722-5 (DE-588)4044779-0 (DE-588)4012251-7 (DE-588)4070505-5 (DE-588)4167717-1 |
| title | Linear partial differential operators |
| title_auth | Linear partial differential operators |
| title_exact_search | Linear partial differential operators |
| title_full | Linear partial differential operators Lars Hörmander |
| title_fullStr | Linear partial differential operators Lars Hörmander |
| title_full_unstemmed | Linear partial differential operators Lars Hörmander |
| title_new | Hörmander, Lars The analysis of linear partial differential operators |
| title_short | Linear partial differential operators |
| title_sort | linear partial differential operators |
| topic | General theory of first order linear PDE General theory of linear higher-order PDE Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Partieller Differentialoperator (DE-588)4173439-7 gnd Linearer partieller Differentialoperator (DE-588)4167722-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Differentialoperator (DE-588)4012251-7 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd Linearer Differentialoperator (DE-588)4167717-1 gnd |
| topic_facet | General theory of first order linear PDE General theory of linear higher-order PDE Lineare partielle Differentialgleichung Partieller Differentialoperator Linearer partieller Differentialoperator Partielle Differentialgleichung Differentialoperator Distribution Funktionalanalysis Linearer Differentialoperator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003940558&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT hormanderlars linearpartialdifferentialoperators |