Convex cones in analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Paris
Hermann
2006
|
| Schriftenreihe: | Collection Travaux en cours
67 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 251 S. |
| ISBN: | 2705666710 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Introduction j;j
Notations and Definitions x
1 Weakly complete convex sets and cones; first properties 1
1.1 Embeddings of weakly complete convex sets in products M7 x
(M+) . Applications 1
1.2 Caps and extreme elements of convex sets belonging to S . . . 5
1.3 Various other topologies on cones belonging to S 7
2 Conical measures, integral representation, caps of cones 11
II. 1 Conical measures on locally convex Hausdorff spaces 11
11.2 Conical measures living on a cone X € S. Maximal conical
measures yj
11.3 Caps of cones; well capped cones 21
11.4 The sub classes Sd and Sm of S 31
11.5 Pseudo caps of cones and conuclear cones of E. Thomas ... 34
11.6 Maximal conical measures and Baire spaces 46
II. 7 Extension of the theorem of Cartier Fell Meyer to conical mea¬
sures 53
3 Applications of caps theory 63
111.1 Bochner Weil s theorem 63
111.2 Bernstein s theorem; generalizations 67
111.3 The convolution equation // * er /z 69
111.4 Invariant measures and capacities on a locally compact Haus¬
dorff space 73
111.5 Brelot s and Bauer s axiomatics in Potential theory 81
111.6 Hypoelliptic operators 93
111.7 Quasi invariant measures on C(R) 95
ii
CONTENTS iii
4 Conical measures and the formalism of statistical decision 101
IV.1 Conical measure associated to a family of probabilities .... 102
IV.2 Formalism of statistical decision 105
IV.3 Interpretation of the relation (A n) in terms of finer obser¬
vations 109
5 Zonoforms, functions of negative type and vector measures 112
V.I Definition of a zonoform; first properties 113
V.2 Functions of negative type and polar of zonoforms 117
V.3 Vector measures and conical measures 123
6 Representation of conical measures 128
VI. 1 Relationships between conical and cylindrical measures .... 128
VI.2 Integration in closed convex cones (proper or not) 134
VI.3 Extension of a conical measure. Applications 139
VI.4 Weakening of the topology of a cone X € S. Applications . . 144
VI.5 The sub classes C and Cs of S 148
7 Bireticulated cones and positive linear forms on spaces of func¬
tions 159
VII. 1 Bireticulated cones and vector lattices 160
VII.2 Shaped and well capped bireticulated cones 168
VII.3 Adapted spaces and bireticulated cones 174
VII.4 Cones (E+) 7 and spaces of continuous functions 178
8 The class S in Banach spaces 184
VIII. 1 Topological properties of the cones X e S contained in a
Banach space or in its dual 184
VIII.2 The class C in Banach spaces 189
VIII.3 Cones with a universal cap contained in the dual of a Banach
space 195
VIII.4 Structure of normal cones contained in Banach spaces .... 201
Appendix 1. Radon measures on arbitrary Hausdorff topological
spaces 213
Appendix 2. Summing and nuclear maps 216
Appendix 3. Factorization of operators with values in an L1 space 218
Appendix 4. Historical comments 220
References 230
iv Convex cones in analysis
Definition index 242
Notation index 246
Postface (by G. Choquet) 248
|
| adam_txt |
Contents
Introduction j;j
Notations and Definitions x
1 Weakly complete convex sets and cones; first properties 1
1.1 Embeddings of weakly complete convex sets in products M7 x
(M+) . Applications 1
1.2 Caps and extreme elements of convex sets belonging to S . . . 5
1.3 Various other topologies on cones belonging to S 7
2 Conical measures, integral representation, caps of cones 11
II. 1 Conical measures on locally convex Hausdorff spaces 11
11.2 Conical measures living on a cone X € S. Maximal conical
measures yj
11.3 Caps of cones; well capped cones 21
11.4 The sub classes Sd and Sm of S 31
11.5 Pseudo caps of cones and conuclear cones of E. Thomas . 34
11.6 Maximal conical measures and Baire spaces 46
II. 7 Extension of the theorem of Cartier Fell Meyer to conical mea¬
sures 53
3 Applications of caps theory 63
111.1 Bochner Weil's theorem 63
111.2 Bernstein's theorem; generalizations 67
111.3 The convolution equation // * er /z 69
111.4 Invariant measures and capacities on a locally compact Haus¬
dorff space 73
111.5 Brelot's and Bauer's axiomatics in Potential theory 81
111.6 Hypoelliptic operators 93
111.7 Quasi invariant measures on C(R) 95
ii
CONTENTS iii
4 Conical measures and the formalism of statistical decision 101
IV.1 Conical measure associated to a family of probabilities . 102
IV.2 Formalism of statistical decision 105
IV.3 Interpretation of the relation (A n) in terms of finer obser¬
vations 109
5 Zonoforms, functions of negative type and vector measures 112
V.I Definition of a zonoform; first properties 113
V.2 Functions of negative type and polar of zonoforms 117
V.3 Vector measures and conical measures 123
6 Representation of conical measures 128
VI. 1 Relationships between conical and cylindrical measures . 128
VI.2 Integration in closed convex cones (proper or not) 134
VI.3 Extension of a conical measure. Applications 139
VI.4 Weakening of the topology of a cone X € S. Applications . . 144
VI.5 The sub classes C and Cs of S 148
7 Bireticulated cones and positive linear forms on spaces of func¬
tions 159
VII. 1 Bireticulated cones and vector lattices 160
VII.2 Shaped and well capped bireticulated cones 168
VII.3 Adapted spaces and bireticulated cones 174
VII.4 Cones (E+)'7' and spaces of continuous functions 178
8 The class S in Banach spaces 184
VIII. 1 Topological properties of the cones X e S contained in a
Banach space or in its dual 184
VIII.2 The class C in Banach spaces 189
VIII.3 Cones with a universal cap contained in the dual of a Banach
space 195
VIII.4 Structure of normal cones contained in Banach spaces . 201
Appendix 1. Radon measures on arbitrary Hausdorff topological
spaces 213
Appendix 2. Summing and nuclear maps 216
Appendix 3. Factorization of operators with values in an L1 space 218
Appendix 4. Historical comments 220
References 230
iv Convex cones in analysis
Definition index 242
Notation index 246
Postface (by G. Choquet) 248 |
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| isbn | 2705666710 |
| language | English |
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| physical | XIII, 251 S. |
| publishDate | 2006 |
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| series | Collection Travaux en cours |
| series2 | Collection Travaux en cours |
| spelling | Becker, Richard Verfasser aut Convex cones in analysis Richard Becker Paris Hermann 2006 XIII, 251 S. txt rdacontent n rdamedia nc rdacarrier Collection Travaux en cours 67 Cone Convex bodies Collection Travaux en cours 67 (DE-604)BV005629478 67 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015966151&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Becker, Richard Convex cones in analysis Collection Travaux en cours Cone Convex bodies |
| title | Convex cones in analysis |
| title_auth | Convex cones in analysis |
| title_exact_search | Convex cones in analysis |
| title_exact_search_txtP | Convex cones in analysis |
| title_full | Convex cones in analysis Richard Becker |
| title_fullStr | Convex cones in analysis Richard Becker |
| title_full_unstemmed | Convex cones in analysis Richard Becker |
| title_short | Convex cones in analysis |
| title_sort | convex cones in analysis |
| topic | Cone Convex bodies |
| topic_facet | Cone Convex bodies |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015966151&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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