Compact Convex Sets and Boundary Integrals:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1971
|
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
57 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The importance of convexity arguments in functional analysis has long been realized, but a comprehensive theory of infinite-dimensional convex sets has hardly existed for more than a decade. In fact, the integral representation theorems of Choquet and Bishop-de Leeuw together with the uniqueness theorem of Choquet inaugurated a new epoch in infinite-dimensional convexity. Initially considered curious and technically difficult, these theorems attracted many mathematicians, and the proofs were gradually simplified and fitted into a general theory. The results can no longer be considered very "deep" or difficult, but they certainly remain all the more important. Today Choquet Theory provides a unified approach to integral representations in fields as diverse as potential theory, probability, function algebras, operator theory, group representations and ergodic theory. At the same time the new concepts and results have made it possible, and relevant, to ask new questions within the abstract theory itself. Such questions pertain to the interplay between compact convex sets K and their associated spaces A(K) of continuous affine functions; to the duality between faces of K and appropriate ideals of A(K); to dominatedextension problems for continuous affine functions on faces; and to direct convex sum decomposition into faces, as well as to integral formulas generalizing such decompositions. These problems are of geometric interest in their own right, but they are primarily suggested by applications, in particular to operator theory and function algebras |
| Physical Description: | 1 Online-Ressource (XII, 212 p) |
| ISBN: | 9783642650093 9783642650116 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-65009-3 |
Staff View
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042422854 | ||
| 003 | DE-604 | ||
| 005 | 20180108 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1971 |||| o||u| ||||||eng d | ||
| 020 | |a 9783642650093 |c Online |9 978-3-642-65009-3 | ||
| 020 | |a 9783642650116 |c Print |9 978-3-642-65011-6 | ||
| 024 | 7 | |a 10.1007/978-3-642-65009-3 |2 doi | |
| 035 | |a (OCoLC)863788570 | ||
| 035 | |a (DE-599)BVBBV042422854 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 510 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Alfsen, Erik M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Compact Convex Sets and Boundary Integrals |c by Erik M. Alfsen |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1971 | |
| 300 | |a 1 Online-Ressource (XII, 212 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete |v 57 |x 0071-1136 | |
| 500 | |a The importance of convexity arguments in functional analysis has long been realized, but a comprehensive theory of infinite-dimensional convex sets has hardly existed for more than a decade. In fact, the integral representation theorems of Choquet and Bishop-de Leeuw together with the uniqueness theorem of Choquet inaugurated a new epoch in infinite-dimensional convexity. Initially considered curious and technically difficult, these theorems attracted many mathematicians, and the proofs were gradually simplified and fitted into a general theory. The results can no longer be considered very "deep" or difficult, but they certainly remain all the more important. Today Choquet Theory provides a unified approach to integral representations in fields as diverse as potential theory, probability, function algebras, operator theory, group representations and ergodic theory. At the same time the new concepts and results have made it possible, and relevant, to ask new questions within the abstract theory itself. Such questions pertain to the interplay between compact convex sets K and their associated spaces A(K) of continuous affine functions; to the duality between faces of K and appropriate ideals of A(K); to dominatedextension problems for continuous affine functions on faces; and to direct convex sum decomposition into faces, as well as to integral formulas generalizing such decompositions. These problems are of geometric interest in their own right, but they are primarily suggested by applications, in particular to operator theory and function algebras | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Mathematics, general | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Konvexität |0 (DE-588)4114284-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Randintegral |0 (DE-588)4607681-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Funktionalanalysis |0 (DE-588)4018916-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Konvexe Menge |0 (DE-588)4165212-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kompakte konvexe Menge |0 (DE-588)4164844-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Choquet-Theorie |0 (DE-588)4638875-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Funktionalanalysis |0 (DE-588)4018916-8 |D s |
| 689 | 0 | 1 | |a Choquet-Theorie |0 (DE-588)4638875-8 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Konvexe Menge |0 (DE-588)4165212-5 |D s |
| 689 | 1 | 1 | |a Randintegral |0 (DE-588)4607681-5 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 689 | 2 | 0 | |a Kompakte konvexe Menge |0 (DE-588)4164844-4 |D s |
| 689 | 2 | |8 3\p |5 DE-604 | |
| 689 | 3 | 0 | |a Konvexität |0 (DE-588)4114284-6 |D s |
| 689 | 3 | |8 4\p |5 DE-604 | |
| 830 | 0 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete |v 57 |w (DE-604)BV005871160 |9 57 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-642-65009-3 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027858271 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 3\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 4\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804153097839181824 |
|---|---|
| any_adam_object | |
| author | Alfsen, Erik M. |
| author_facet | Alfsen, Erik M. |
| author_role | aut |
| author_sort | Alfsen, Erik M. |
| author_variant | e m a em ema |
| building | Verbundindex |
| bvnumber | BV042422854 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863788570 (DE-599)BVBBV042422854 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-65009-3 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04134nmm a2200649zcb4500</leader><controlfield tag="001">BV042422854</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20180108 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1971 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642650093</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-642-65009-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642650116</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-642-65011-6</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-642-65009-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863788570</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042422854</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Alfsen, Erik M.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Compact Convex Sets and Boundary Integrals</subfield><subfield code="c">by Erik M. Alfsen</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">1971</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XII, 212 p)</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">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Ergebnisse der Mathematik und ihrer Grenzgebiete</subfield><subfield code="v">57</subfield><subfield code="x">0071-1136</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">The importance of convexity arguments in functional analysis has long been realized, but a comprehensive theory of infinite-dimensional convex sets has hardly existed for more than a decade. In fact, the integral representation theorems of Choquet and Bishop-de Leeuw together with the uniqueness theorem of Choquet inaugurated a new epoch in infinite-dimensional convexity. Initially considered curious and technically difficult, these theorems attracted many mathematicians, and the proofs were gradually simplified and fitted into a general theory. The results can no longer be considered very "deep" or difficult, but they certainly remain all the more important. Today Choquet Theory provides a unified approach to integral representations in fields as diverse as potential theory, probability, function algebras, operator theory, group representations and ergodic theory. At the same time the new concepts and results have made it possible, and relevant, to ask new questions within the abstract theory itself. Such questions pertain to the interplay between compact convex sets K and their associated spaces A(K) of continuous affine functions; to the duality between faces of K and appropriate ideals of A(K); to dominatedextension problems for continuous affine functions on faces; and to direct convex sum decomposition into faces, as well as to integral formulas generalizing such decompositions. These problems are of geometric interest in their own right, but they are primarily suggested by applications, in particular to operator theory and function algebras</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Konvexität</subfield><subfield code="0">(DE-588)4114284-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Randintegral</subfield><subfield code="0">(DE-588)4607681-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Konvexe Menge</subfield><subfield code="0">(DE-588)4165212-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kompakte konvexe Menge</subfield><subfield code="0">(DE-588)4164844-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Choquet-Theorie</subfield><subfield code="0">(DE-588)4638875-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Choquet-Theorie</subfield><subfield code="0">(DE-588)4638875-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Konvexe Menge</subfield><subfield code="0">(DE-588)4165212-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Randintegral</subfield><subfield code="0">(DE-588)4607681-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Kompakte konvexe Menge</subfield><subfield code="0">(DE-588)4164844-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">3\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="3" ind2="0"><subfield code="a">Konvexität</subfield><subfield code="0">(DE-588)4114284-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2=" "><subfield code="8">4\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Ergebnisse der Mathematik und ihrer Grenzgebiete</subfield><subfield code="v">57</subfield><subfield code="w">(DE-604)BV005871160</subfield><subfield code="9">57</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-642-65009-3</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027858271</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">3\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">4\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042422854 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642650093 9783642650116 |
| issn | 0071-1136 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858271 |
| oclc_num | 863788570 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XII, 212 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spelling | Alfsen, Erik M. Verfasser aut Compact Convex Sets and Boundary Integrals by Erik M. Alfsen Berlin, Heidelberg Springer Berlin Heidelberg 1971 1 Online-Ressource (XII, 212 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 57 0071-1136 The importance of convexity arguments in functional analysis has long been realized, but a comprehensive theory of infinite-dimensional convex sets has hardly existed for more than a decade. In fact, the integral representation theorems of Choquet and Bishop-de Leeuw together with the uniqueness theorem of Choquet inaugurated a new epoch in infinite-dimensional convexity. Initially considered curious and technically difficult, these theorems attracted many mathematicians, and the proofs were gradually simplified and fitted into a general theory. The results can no longer be considered very "deep" or difficult, but they certainly remain all the more important. Today Choquet Theory provides a unified approach to integral representations in fields as diverse as potential theory, probability, function algebras, operator theory, group representations and ergodic theory. At the same time the new concepts and results have made it possible, and relevant, to ask new questions within the abstract theory itself. Such questions pertain to the interplay between compact convex sets K and their associated spaces A(K) of continuous affine functions; to the duality between faces of K and appropriate ideals of A(K); to dominatedextension problems for continuous affine functions on faces; and to direct convex sum decomposition into faces, as well as to integral formulas generalizing such decompositions. These problems are of geometric interest in their own right, but they are primarily suggested by applications, in particular to operator theory and function algebras Mathematics Mathematics, general Mathematik Konvexität (DE-588)4114284-6 gnd rswk-swf Randintegral (DE-588)4607681-5 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Konvexe Menge (DE-588)4165212-5 gnd rswk-swf Kompakte konvexe Menge (DE-588)4164844-4 gnd rswk-swf Choquet-Theorie (DE-588)4638875-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s Choquet-Theorie (DE-588)4638875-8 s 1\p DE-604 Konvexe Menge (DE-588)4165212-5 s Randintegral (DE-588)4607681-5 s 2\p DE-604 Kompakte konvexe Menge (DE-588)4164844-4 s 3\p DE-604 Konvexität (DE-588)4114284-6 s 4\p DE-604 Ergebnisse der Mathematik und ihrer Grenzgebiete 57 (DE-604)BV005871160 57 https://doi.org/10.1007/978-3-642-65009-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Alfsen, Erik M. Compact Convex Sets and Boundary Integrals Ergebnisse der Mathematik und ihrer Grenzgebiete Mathematics Mathematics, general Mathematik Konvexität (DE-588)4114284-6 gnd Randintegral (DE-588)4607681-5 gnd Funktionalanalysis (DE-588)4018916-8 gnd Konvexe Menge (DE-588)4165212-5 gnd Kompakte konvexe Menge (DE-588)4164844-4 gnd Choquet-Theorie (DE-588)4638875-8 gnd |
| subject_GND | (DE-588)4114284-6 (DE-588)4607681-5 (DE-588)4018916-8 (DE-588)4165212-5 (DE-588)4164844-4 (DE-588)4638875-8 |
| title | Compact Convex Sets and Boundary Integrals |
| title_auth | Compact Convex Sets and Boundary Integrals |
| title_exact_search | Compact Convex Sets and Boundary Integrals |
| title_full | Compact Convex Sets and Boundary Integrals by Erik M. Alfsen |
| title_fullStr | Compact Convex Sets and Boundary Integrals by Erik M. Alfsen |
| title_full_unstemmed | Compact Convex Sets and Boundary Integrals by Erik M. Alfsen |
| title_short | Compact Convex Sets and Boundary Integrals |
| title_sort | compact convex sets and boundary integrals |
| topic | Mathematics Mathematics, general Mathematik Konvexität (DE-588)4114284-6 gnd Randintegral (DE-588)4607681-5 gnd Funktionalanalysis (DE-588)4018916-8 gnd Konvexe Menge (DE-588)4165212-5 gnd Kompakte konvexe Menge (DE-588)4164844-4 gnd Choquet-Theorie (DE-588)4638875-8 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Konvexität Randintegral Funktionalanalysis Konvexe Menge Kompakte konvexe Menge Choquet-Theorie |
| url | https://doi.org/10.1007/978-3-642-65009-3 |
| volume_link | (DE-604)BV005871160 |
| work_keys_str_mv | AT alfsenerikm compactconvexsetsandboundaryintegrals |