Positive polynomials: from Hilbert's 17th problem to real algebra
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer
[2001]
|
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | VIII, 267 Seiten Illustrationen |
| ISBN: | 9783540412151 3540412158 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV013588564 | ||
| 003 | DE-604 | ||
| 005 | 20201202 | ||
| 007 | t | ||
| 008 | 010214s2001 a||| |||| 00||| eng d | ||
| 016 | 7 | |a 961038322 |2 DE-101 | |
| 020 | |a 9783540412151 |9 978-3-540-41215-1 | ||
| 020 | |a 3540412158 |9 3-540-41215-8 | ||
| 035 | |a (OCoLC)248354499 | ||
| 035 | |a (DE-599)BVBBV013588564 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-739 |a DE-355 |a DE-20 |a DE-91G |a DE-824 |a DE-384 |a DE-706 |a DE-19 |a DE-83 |a DE-11 |a DE-188 |a DE-634 | ||
| 050 | 0 | |a QA161.P59 | |
| 082 | 0 | |a 512 | |
| 084 | |a SK 230 |0 (DE-625)143225: |2 rvk | ||
| 084 | |a 12D15 |2 msc | ||
| 084 | |a 12J15 |2 msc | ||
| 084 | |a MAT 120f |2 stub | ||
| 100 | 1 | |a Prestel, Alexander |d 1941-2024 |e Verfasser |0 (DE-588)117718777 |4 aut | |
| 245 | 1 | 0 | |a Positive polynomials |b from Hilbert's 17th problem to real algebra |c Alexander Prestel, Charles N. Delzell |
| 264 | 1 | |a Berlin |b Springer |c [2001] | |
| 300 | |a VIII, 267 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer monographs in mathematics | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Positives Polynom | |
| 650 | 4 | |a Reelle Algebra | |
| 650 | 4 | |a Semialgebraische Menge | |
| 650 | 4 | |a Topologischer Körper | |
| 650 | 4 | |a Polynomials | |
| 650 | 4 | |a Semialgebraic sets | |
| 650 | 4 | |a Topological fields | |
| 650 | 0 | 7 | |a Topologischer Körper |0 (DE-588)4242582-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Semialgebraische Menge |0 (DE-588)4382209-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Reelle Algebra |0 (DE-588)4225009-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Positives Polynom |0 (DE-588)4193849-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Reelle Algebra |0 (DE-588)4225009-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Positives Polynom |0 (DE-588)4193849-5 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Topologischer Körper |0 (DE-588)4242582-7 |D s |
| 689 | 2 | |5 DE-604 | |
| 689 | 3 | 0 | |a Semialgebraische Menge |0 (DE-588)4382209-5 |D s |
| 689 | 3 | |5 DE-604 | |
| 700 | 1 | |a Delzell, Charles N. |d 1953- |e Verfasser |0 (DE-588)173395597 |4 aut | |
| 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=009280521&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009280521 | ||
Datensatz im Suchindex
| _version_ | 1804128390788153344 |
|---|---|
| adam_text | Contents
Introduction 1
1. Real Fields 7
1.1 Ordered Fields 7
1.2 Extensions of Orderings 12
1.3 The Real Closure 16
1.4 Exercises 24
1.5 Bibliographical and Historical Comments 28
2. Semialgebraic Sets 31
2.1 Semialgebraic Sets 31
2.2 Ultraproducts 36
2.3 Elimination of Quantifiers 41
2.4 The Finiteness Theorem 45
2.5 Exercises 47
2.6 Bibliographical and Historical Comments 48
3. Quadratic Forms over Real Fields 53
3.1 Witt Decomposition 53
3.2 The Witt Ring of a Field 59
3.3 Signatures 62
3.4 Quadratic Forms Over Real Function Fields 68
3.5 Generalization of Hilbert s 17th Problem 74
3.6 Exercises 77
3.7 Bibliographical and Historical Comments 79
4. Real Rings 81
4.1 The Real Spectrum of a Commutative Ring 81
4.2 The Positivstellensatz 86
4.3 Continuous Representation of Polynomials 91
4.4 ^ Fields 94
4.5 The Real Spectrum of M[Xx,...,Xn] 101
4.6 Exercises 107
4.7 Bibliographical and Historical Comments 109
VIII Contents
5. Archimedean Rings 113
5.1 Quadratic Modules and Semiorderings 113
5.2 Rings with Archimedean Preorderings 119
5.3 Rings with Archimedean Quadratic Modules 124
5.4 Rings with Archimedean Preprimes 130
5.5 Exercises 134
5.6 Bibliographical and Historical Comments 136
6. Positive Polynomials on Semialgebraic Sets 139
6.1 Semiorderings and Weak Isotropy 139
6.2 Archimedean Quadratic Modules on E[Xi,...,Xn] 142
6.3 Distinguished Representations of Positive Polynomials 145
6.4 Applications to the Moment Problem 152
6.5 Exercises 157
6.6 Bibliographical and Historical Comments 158
7. Sums of 2mth Powers 161
7.1 Preorderings and Semiorderings of Level 2m 161
7.2 Semiorderings of Level 2m on Fields 166
7.3 Archimedean Modules of Level 2m 169
7.4 Exercises 176
7.5 Bibliographical and Historical Comments 177
8. Bounds 179
8.1 Length of Sums of Squares 179
8.2 Existence of Degree Bounds 183
8.3 Positive Polynomials over Non Archimedean Fields 189
8.4 Distinguished Representations in the Non Archimedean Case. 196
8.5 Exercise 201
8.6 Bibliographical and Historical Comments 201
Appendix: Valued Fields 203
A.I Valuations 203
A.2 Algebraic Extensions 207
A.3 Henselian Fields 213
A.4 Complete Fields 223
A.5 Dependence and Composition of Valuations 230
A.6 Transcendental Extensions 236
A.7 Exercises 242
A.8 Bibliographical Comments 245
References 247
Glossary of Notations 255
Index 259
|
| any_adam_object | 1 |
| author | Prestel, Alexander 1941-2024 Delzell, Charles N. 1953- |
| author_GND | (DE-588)117718777 (DE-588)173395597 |
| author_facet | Prestel, Alexander 1941-2024 Delzell, Charles N. 1953- |
| author_role | aut aut |
| author_sort | Prestel, Alexander 1941-2024 |
| author_variant | a p ap c n d cn cnd |
| building | Verbundindex |
| bvnumber | BV013588564 |
| callnumber-first | Q - Science |
| callnumber-label | QA161 |
| callnumber-raw | QA161.P59 |
| callnumber-search | QA161.P59 |
| callnumber-sort | QA 3161 P59 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 |
| classification_tum | MAT 120f |
| ctrlnum | (OCoLC)248354499 (DE-599)BVBBV013588564 |
| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02420nam a2200625 c 4500</leader><controlfield tag="001">BV013588564</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20201202 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">010214s2001 a||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">961038322</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783540412151</subfield><subfield code="9">978-3-540-41215-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540412158</subfield><subfield code="9">3-540-41215-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)248354499</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV013588564</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</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-355</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA161.P59</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 230</subfield><subfield code="0">(DE-625)143225:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">12D15</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">12J15</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 120f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Prestel, Alexander</subfield><subfield code="d">1941-2024</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)117718777</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Positive polynomials</subfield><subfield code="b">from Hilbert's 17th problem to real algebra</subfield><subfield code="c">Alexander Prestel, Charles N. Delzell</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin</subfield><subfield code="b">Springer</subfield><subfield code="c">[2001]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VIII, 267 Seiten</subfield><subfield code="b">Illustrationen</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="0" ind2=" "><subfield code="a">Springer monographs in mathematics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Hier auch später erschienene, unveränderte Nachdrucke</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Positives Polynom</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Reelle Algebra</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Semialgebraische Menge</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Topologischer Körper</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Polynomials</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Semialgebraic sets</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Topological fields</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Topologischer Körper</subfield><subfield code="0">(DE-588)4242582-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Semialgebraische Menge</subfield><subfield code="0">(DE-588)4382209-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Reelle Algebra</subfield><subfield code="0">(DE-588)4225009-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Positives Polynom</subfield><subfield code="0">(DE-588)4193849-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Reelle Algebra</subfield><subfield code="0">(DE-588)4225009-2</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">Positives Polynom</subfield><subfield code="0">(DE-588)4193849-5</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">Topologischer Körper</subfield><subfield code="0">(DE-588)4242582-7</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">Semialgebraische Menge</subfield><subfield code="0">(DE-588)4382209-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Delzell, Charles N.</subfield><subfield code="d">1953-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)173395597</subfield><subfield code="4">aut</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=009280521&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:BVB01-009280521</subfield></datafield></record></collection> |
| id | DE-604.BV013588564 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:48:29Z |
| institution | BVB |
| isbn | 9783540412151 3540412158 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009280521 |
| oclc_num | 248354499 |
| open_access_boolean | |
| owner | DE-739 DE-355 DE-BY-UBR DE-20 DE-91G DE-BY-TUM DE-824 DE-384 DE-706 DE-19 DE-BY-UBM DE-83 DE-11 DE-188 DE-634 |
| owner_facet | DE-739 DE-355 DE-BY-UBR DE-20 DE-91G DE-BY-TUM DE-824 DE-384 DE-706 DE-19 DE-BY-UBM DE-83 DE-11 DE-188 DE-634 |
| physical | VIII, 267 Seiten Illustrationen |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spelling | Prestel, Alexander 1941-2024 Verfasser (DE-588)117718777 aut Positive polynomials from Hilbert's 17th problem to real algebra Alexander Prestel, Charles N. Delzell Berlin Springer [2001] VIII, 267 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Hier auch später erschienene, unveränderte Nachdrucke Positives Polynom Reelle Algebra Semialgebraische Menge Topologischer Körper Polynomials Semialgebraic sets Topological fields Topologischer Körper (DE-588)4242582-7 gnd rswk-swf Semialgebraische Menge (DE-588)4382209-5 gnd rswk-swf Reelle Algebra (DE-588)4225009-2 gnd rswk-swf Positives Polynom (DE-588)4193849-5 gnd rswk-swf Reelle Algebra (DE-588)4225009-2 s DE-604 Positives Polynom (DE-588)4193849-5 s Topologischer Körper (DE-588)4242582-7 s Semialgebraische Menge (DE-588)4382209-5 s Delzell, Charles N. 1953- Verfasser (DE-588)173395597 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009280521&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Prestel, Alexander 1941-2024 Delzell, Charles N. 1953- Positive polynomials from Hilbert's 17th problem to real algebra Positives Polynom Reelle Algebra Semialgebraische Menge Topologischer Körper Polynomials Semialgebraic sets Topological fields Topologischer Körper (DE-588)4242582-7 gnd Semialgebraische Menge (DE-588)4382209-5 gnd Reelle Algebra (DE-588)4225009-2 gnd Positives Polynom (DE-588)4193849-5 gnd |
| subject_GND | (DE-588)4242582-7 (DE-588)4382209-5 (DE-588)4225009-2 (DE-588)4193849-5 |
| title | Positive polynomials from Hilbert's 17th problem to real algebra |
| title_auth | Positive polynomials from Hilbert's 17th problem to real algebra |
| title_exact_search | Positive polynomials from Hilbert's 17th problem to real algebra |
| title_full | Positive polynomials from Hilbert's 17th problem to real algebra Alexander Prestel, Charles N. Delzell |
| title_fullStr | Positive polynomials from Hilbert's 17th problem to real algebra Alexander Prestel, Charles N. Delzell |
| title_full_unstemmed | Positive polynomials from Hilbert's 17th problem to real algebra Alexander Prestel, Charles N. Delzell |
| title_short | Positive polynomials |
| title_sort | positive polynomials from hilbert s 17th problem to real algebra |
| title_sub | from Hilbert's 17th problem to real algebra |
| topic | Positives Polynom Reelle Algebra Semialgebraische Menge Topologischer Körper Polynomials Semialgebraic sets Topological fields Topologischer Körper (DE-588)4242582-7 gnd Semialgebraische Menge (DE-588)4382209-5 gnd Reelle Algebra (DE-588)4225009-2 gnd Positives Polynom (DE-588)4193849-5 gnd |
| topic_facet | Positives Polynom Reelle Algebra Semialgebraische Menge Topologischer Körper Polynomials Semialgebraic sets Topological fields |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009280521&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT prestelalexander positivepolynomialsfromhilberts17thproblemtorealalgebra AT delzellcharlesn positivepolynomialsfromhilberts17thproblemtorealalgebra |