Positive polynomials and sums of squares:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2008]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 146 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016488684&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xii, 187 Seiten Diagramme |
| ISBN: | 9780821844021 0821844024 |
Internformat
MARC
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|---|---|---|---|
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| 100 | 1 | |a Marshall, Murray |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Positive polynomials and sums of squares |c Murray Marshall |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2008] | |
| 264 | 4 | |c © 2008 | |
| 300 | |a xii, 187 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v Volume 146 | |
| 650 | 7 | |a Cálculo operacional |2 larpcal | |
| 650 | 7 | |a Geometria algébrica real |2 larpcal | |
| 650 | 4 | |a Géométrie algébrique | |
| 650 | 4 | |a Optimisation mathématique | |
| 650 | 7 | |a Otimização matemática |2 larpcal | |
| 650 | 4 | |a Polynômes | |
| 650 | 4 | |a Problèmes des moments (Mathématiques) | |
| 650 | 7 | |a Programação matemática |2 larpcal | |
| 650 | 4 | |a Moment problems (Mathematics) | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 4 | |a Polynomials | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 0 | 7 | |a Polynomapproximation |0 (DE-588)4197097-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
| 689 | 0 | 1 | |a Polynomapproximation |0 (DE-588)4197097-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-1373-6 |
| 830 | 0 | |a Mathematical surveys and monographs |v Volume 146 |w (DE-604)BV000018014 |9 146 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016488684&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016488684 | |
Datensatz im Suchindex
| _version_ | 1819284778583588864 |
|---|---|
| adam_text | Contents
Preface
vu
Introduction
ix
Chapter
0.
Preliminaries
1
0.1
Notations
1
0.2
Positive
Semidefinite
Matrices
1
Chapter
1.
Positive Polynomials and Sums of Squares
3
1.1
Preliminaries on Polynomials
3
1.2
Positive Polynomials
4
1.3
Extending Positive Polynomials
8
1.4
Hubert s 17th Problem
11
1.5
Baer-Krull Theorem
14
1.6
Formal Power Series Rings
17
Chapter
2.
Krivine s
Positivstellensatz 21
2.1
Quadratic Modules and Preorderings
21
2.2 Positivstellensatz 25
2.3
The Proof
27
2.4
The Real Spectrum
29
2.5
Abstract
Positivstellensatz 31
2.6
Saturation
33
2.7
Low-Dimensional Examples
35
Chapter
3.
The Moment Problem
41
3.1
Introduction
41
3.2
Proof of Haviland s Theorem
44
3.3
Uniqueness Question
46
3.4
The Conditions (SMP) and (MP)
47
3.5
Schrmidgen s Theorem
48
3.6
Countable Dimensional Vector Spaces
50
Chapter
4.
Non-Compact Case
55
4.1
Stability
55
4.2
Examples where (SMP) and (MP) fail
61
4.3
Examples where (SMP) and (MP) hold
64
4.4
Direct Integral Decomposition
65
Chapter
5.
Archimedean T-modules
71
5.1
Preprimes
71
iii
iv CONTENTS
5.2
Т
-modules
72
5.3 Semiorderings
and Valuations
75
5.4
Representation
Theorem 78
5.5 Theorems
of
Pólya
and Reznick
80
5.6
Other
Applications
83
5.7
Topology on
Va
=
Ηοηι(Α,Κ)
84
Chapter
6. Schmüdgen s Positivstellensatz 87
6.1
Wörmann s
Trick 87
6.2
Non-Compact Case
89
6.3
Remarks and Examples
92
Chapter
7.
Putinar s Question
97
7.1
Introduction
97
7.2
Stable Compactness
100
7.3
Jacobi-Prestel Counterexample
103
7.4
The Case dim J^M
< 1 105
Chapter
8.
Weak Isotropy of Quadratic Forms
109
8.1
Isotropy and Weak Isotropy
109
8.2
Residue Forms
110
8.3
Local-Global Principle for Weak Isotropy
113
8.4
Pfister Forms
116
8.5
Application to Putinar s Question
117
Chapter
9.
Scheiderer s Local-Global Principle
123
9.1
Basic Lemma
123
9.2
Local-Global Principle
125
9.3
The Case
η
= 1 128
9.4
The Case
η
= 2 130
9.5
Hessian Conditions
133
9.6
Second Local-Global Principle
134
Chapter
10.
Semidefinite Programming and Optimization
137
10.1
The Cone of PSD Matrices
137
10.2
Semideñnite
Programming
138
10.3
Max-Cut Problem
142
10.4
Global Optimization
145
10.5
Constrained Optimization
148
10.6
Exploiting the Gradient Ideal
151
10.7
Existence of Feasible Solutions
156
Appendix
1.
Tarski-Seidenberg Theorem
161
11.1
Basic Version
161
11.2
Tarski s Transfer Principle
162
11.3
Lang s Homomorphism Theorem
163
11.4
Geometric Version
165
11.5
General Version
167
Appendix
2.
Algebraic Sets
169
12.1
Transcendence Degree and Krull Dimension
169
CONTENTS v
12.2
Non-Singular Zeros
171
12.3
Algebraic Sets
173
12.4
Dimension
175
12.5
Radical Ideals and Real Ideals
177
12.6
Simple Point Criterion
178
12.7
Sign-Changing Criterion
178
Bibliography
183
|
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 SK 240 |
| ctrlnum | (OCoLC)175286448 (DE-599)BVBBV023304286 |
| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
| dewey-search | 516.3/5 |
| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV023304286 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T13:13:03Z |
| institution | BVB |
| isbn | 9780821844021 0821844024 |
| language | English |
| lccn | 2007060573 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016488684 |
| oclc_num | 175286448 |
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| owner_facet | DE-20 DE-355 DE-BY-UBR DE-824 DE-634 DE-739 DE-11 DE-188 DE-19 DE-BY-UBM DE-29T |
| physical | xii, 187 Seiten Diagramme |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spellingShingle | Marshall, Murray Positive polynomials and sums of squares Mathematical surveys and monographs Cálculo operacional larpcal Geometria algébrica real larpcal Géométrie algébrique Optimisation mathématique Otimização matemática larpcal Polynômes Problèmes des moments (Mathématiques) Programação matemática larpcal Moment problems (Mathematics) Geometry, Algebraic Polynomials Mathematical optimization Polynomapproximation (DE-588)4197097-4 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4197097-4 (DE-588)4001161-6 |
| title | Positive polynomials and sums of squares |
| title_auth | Positive polynomials and sums of squares |
| title_exact_search | Positive polynomials and sums of squares |
| title_full | Positive polynomials and sums of squares Murray Marshall |
| title_fullStr | Positive polynomials and sums of squares Murray Marshall |
| title_full_unstemmed | Positive polynomials and sums of squares Murray Marshall |
| title_short | Positive polynomials and sums of squares |
| title_sort | positive polynomials and sums of squares |
| topic | Cálculo operacional larpcal Geometria algébrica real larpcal Géométrie algébrique Optimisation mathématique Otimização matemática larpcal Polynômes Problèmes des moments (Mathématiques) Programação matemática larpcal Moment problems (Mathematics) Geometry, Algebraic Polynomials Mathematical optimization Polynomapproximation (DE-588)4197097-4 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Cálculo operacional Geometria algébrica real Géométrie algébrique Optimisation mathématique Otimização matemática Polynômes Problèmes des moments (Mathématiques) Programação matemática Moment problems (Mathematics) Geometry, Algebraic Polynomials Mathematical optimization Polynomapproximation Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016488684&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT marshallmurray positivepolynomialsandsumsofsquares |