| 词条 | Hans Rådström |
| 释义 |
|name = Hans Rådström |image = |image_size = |caption = |birth_date = 1919 |birth_place = |death_date = 1970 |death_place = |residence = |citizenship = Sweden |nationality = |ethnicity = |fields = Functional equations, set-valued analysis |workplaces = Institute for Advanced Studies, Princeton University; Stockholm University; Linköping University |alma_mater = Stockholm University |doctoral_advisor = Torsten Carleman, Fritz Carlson |academic_advisors = |doctoral_students = Per Enflo |notable_students = |known_for = Rådström isometric embedding of convex subsets in the positive cone of the Lebesgue space of absolutely integrable functions; Rådström characterization of convex sets as generators of continuous semigroups of subsets |influences = Werner Fenchel Andrew Gleason |influenced = Karl Johan Åström[1] |awards = |religion = |signature = |footnotes = }}Hans Vilhem Rådström (1919–1970) was a Swedish mathematician who worked on complex analysis, continuous groups, convex sets, set-valued analysis, and game theory. From 1952, he was lektor (assistant professor) at Stockholm University,[2] and from 1969, he was Professor of Applied Mathematics at Linköping University.[3] Early lifeHans Rådström was the son of the writer and editor Karl Johan Rådström, and the elder brother of the writer and journalist Pär Rådström. Rådström studied mathematics and obtained his Ph.D. under the joint supervision of Torsten Carleman and Fritz Carlson. His early work pertained to the theory of functions of a complex variable, particularly, complex dynamics. He was appointed lektor (assistant professor) at Stockholm University in 1952.[2] Later, he was associated with the Royal Institute of Technology in Stockholm. In 1952 he became co-editor of the Scandinavian popular-mathematics journal Nordisk Matematisk Tidskrift.[4] He also edited the Swedish edition of The Scientific American Book of Mathematical Puzzles and Diversions, a recreational mathematics book by Martin Gardner.[5] Set-valued analysisRådström was interested in Hilbert's fifth problem on the analyticity of the continuous operation of topological groups. The solution of this problem by Andrew Gleason used constructions of subsets of topological vector spaces,[6] (rather than simply points), and inspired Rådström's research on set-valued analysis. He visited the Institute for Advanced Study (IAS) in Princeton from 1948 to 1950,[7] where he co-organized a seminar on convexity.[8] Together with Olof Hanner, who, like Rådström, would earn his Ph.D. from Stockholm University in 1952, he improved Werner Fenchel's version of Carathéodory's lemma.[9] In the 1950s, he obtained important results on convex sets. He proved the Rådström embedding theorem, which implies that the collection of all nonempty compact convex subsets of a normed real vector-space (endowed with the Hausdorff distance) can be isometrically embedded as a convex cone in a normed real vector-space. Under the embedding, the nonempty compact convex sets are mapped to points in the range space. In Rådström's construction, this embedding is additive and positively homogeneous.[11] Rådström's approach used ideas from the theory of topological semi-groups.[10] Later, Lars Hörmander proved a variant of this theorem for locally convex topological vector spaces using the support function (of convex analysis); in Hörmander's approach, the range of the embedding was the Banach lattice L1, and the embedding was isotone.[11][10][12] Rådström characterized the generators of continuous semigroups of sets as compact convex sets.[13] StudentsRådström's Ph.D. students included Per Enflo and Martin Ribe, both of whom wrote Ph.D. theses in functional analysis. In the uniform and Lipschitz categories of topological vector spaces, Enflo's results[14] concerned spaces with local convexity, especially Banach spaces.[15][16] In 1970,[18] Hans Rådström died of a heart attack.[19] Enflo supervised one of Rådström's Linköping students, Lars-Erik Andersson, from 1970–1971, helping him with his 1972 thesis,[19] On connected subgroups of Banach spaces, on Hilbert's fifth problem for complete, normed spaces. The Swedish functional analyst Edgar Asplund, then Professor of Mathematics at Aarhus University in Denmark, assisted Ribe as supervisor of his 1972 thesis,[20] before dying of cancer in 1974.[21] Ribe's results concerned topological vector spaces without assuming local convexity;[15] Ribe constructed a counter-example to naive extensions of the Hahn–Banach theorem to topological vector spaces that lack local convexity.[22] References1. ^{{cite web |url=http://www.tekniskamuseet.se/download/18.6aa228912529fe96108000358/3_Karl_Johan_%C3%85str%C3%B6m.pdf |title=Karl Johan Åström: En intervju av Per Lundin |language=Swedish |trans-title=Karl Johan Åström: An Interview with Per Lundin |date=3 October 2007 |accessdate=29 December 2011 |publisher=teknishkamuseet.se}} 2. ^1 {{cite journal|title=Notes|journal=Bulletin of the American Mathematical Society|volume=58|issue=6|year=1952|pages=683–692|url=http://projecteuclid.org/euclid.bams/1183517444|doi=10.1090/s0002-9904-1952-09670-1 }} 3. ^{{cite web |url=http://www.mai.liu.se/~akbjo/collqmai.pdf |title=LiTH—från plan till verklighet, Åke Björck |language=Swedish |date=27 January 2010 |accessdate=29 December 2011 |publisher=Linköping University |deadurl=yes |archiveurl=https://web.archive.org/web/20120406081320/http://www.mai.liu.se/~akbjo/collqmai.pdf |archivedate=6 April 2012 |df= }} (Webpage of Professor Åke Björck at Linköping University) 4. ^{{cite journal|last=Branner |first=Bodil|authorlink= Bodil Branner |title=On the Foundation of Mathematica Scandinavica|url=http://www.matilde.mathematics.dk/arkiv/M17/Branner_Math_Scand.pdf |journal=Mathematica Scandinavica |volume=93 |year=2003 |pages=5–18|doi=10.7146/math.scand.a-14409}} 5. ^{{cite book|last=Gardner|first=M.|author-link=Martin Gardner|title=Rolig Matematik: Tankenötter och Problem, Andra Samlingen|publisher=Natur & Kultur|location=Stockholm|year=1961}}, see {{cite web|url=https://www.bibliotekenisollentuna.se/web/arena/skaffa-bibliotekskort |title=library card|publisher=Sollentuna library }} 6. ^{{cite book|first=Andrew |last=Gleason|author-link=Andrew Gleason|chapter=One-parameter subgroups and Hilbert's fifth problem|pages=451–452|volume=2|title=Proceedings of the International Congress of Mathematicians, Cambridge, Massachusetts, 1950|location=Providence, Rhode Island|publisher=American Mathematical Society|year=1952}} 7. ^{{cite web|url=http://www.math.ias.edu/people/past-alpha?letter=R|title=Past Members Alphabetical: R|publisher=Institute for Advanced Study|year=2011|accessdate=29 December 2011}} 8. ^{{cite journal|mr=0064421|last1=Bateman|first1=P. T.|authorlink1=Paul T. Bateman |last2=Rådström|first2=Hans|last3=Hanner|first3=Olaf|author3-link=Olof Hanner|last4=Macbeath|first4=A. M.|authorlink4=A. M. Macbeath|last5=Rogers|first5=C. A.|authorlink5=Claude Ambrose Rogers|last6=Pettis|first6=B. J.|authorlink6=B. J. Pettis|last7=Klee|first7=V. L.|authorlink7=Victor Klee|title=Seminar on convex sets, 1949–1950|publisher=The Institute for Advanced Study|location=Princeton, N. J.}} 9. ^{{cite journal|title=Generalizations of a theorem of Carathéodory|first=John R.|last=Reay|journal=Mem. Amer. Math. Soc.|volume=54|year=1965|ref=harv|mr=0188891|institution=Mathematics Department, University of Washington|format=Doctoral thesis}} 10. ^1 {{cite journal|last=Schmidt|first=Klaus D|journal=Acta Applicandae Mathematicae|volume=5|issue=3|pages=209–237|doi=10.1007/BF00047343|mr=|title=Embedding theorems for classes of convex sets|date=March 1986|ref=harv}} 11. ^1 {{harvtxt|Schneider|1993|loc=Notes for section 1.8 (pp. 56–61, especially 57–58)}}: {{cite book|last=Schneider|first=Rolf|title=Convex bodies: The Brunn–Minkowski theory|series=Encyclopedia of mathematics and its applications|volume=44|publisher=Cambridge University Press|location=Cambridge|year=1993|pages=xiv+490 |isbn=978-0-521-35220-8|mr=1216521|ref=harv}} 12. ^{{cite book|mr=1301332|last=Hörmander|first=Lars|title=Notions of convexity|series=Progress in Mathematics|volume=127|publisher=Birkhäuser Boston, Inc.|location=Boston, MA|year=1994|isbn=978-0-8176-3799-6}} 13. ^{{cite book|title=Lie groups, convex cones, and semigroups|last1=Hilgert|first1=Joachim|authorlink1=Joachim Hilgert|last2=Hofmann|first2=Karl Heinrich|authorlink2=Karl Heinrich Hofmann|last3=Lawson|first3=Jimmie D.|authorlink3=Jimmie D. Lawson|isbn=978-0-19-853569-0|lccn=89009289|series=Oxford Mathematical Monographs|url=https://books.google.com/?id=TbyxAAAAIAAJ&q=Radstrom#search_anchor|year=1989|publisher=Oxford University Press|ref=harv}} 14. ^{{cite book|last=Enflo|first=Per|author-link=per Enflo|year=1970|title=Investigations on Hilbert's fifth problem for non locally compact groups|publisher=Stockholm University|format=doctoral thesis}} 15. ^1 {{cite book|last1=Lindensrauss|first1=Joram|author1-link=Joram Lindenstrauss|last2=Benyamini|first2=Yoav|title=Geometric nonlinear functional analysis|series=Colloquium publications|volume=48|publisher=American Mathematical Society}} 16. ^{{cite book|authorlink=Jiří Matoušek (mathematician)|last=Matoušek|first=Jiří|title=Lectures on Discrete Geometry|url=http://kam.mff.cuni.cz/~matousek/dg-nmetr.ps.gz|publisher=Springer-Verlag|series=Graduate Texts in Mathematics|year=2002|isbn=978-0-387-95373-1}} 17. ^* Enflo, Per. (1970) Investigations on Hilbert’s fifth problem for non locally compact groups (Stockholm University). Enflo's thesis contains reprints of exactly five papers** Enflo, Per; 1969a: Topological groups in which multiplication on one side is differentiable or linear. Math. Scand., 24, pp. 195–197. **Enflo, Per; 1969: On the non-existence of uniform homeomorphisms between Lp-spaces. Ark. Mat., 8, s. 103–105. ** {{cite journal|doi=10.1007/BF02589549|author=Per Enflo|title=On the nonexistence of uniform homeomorphisms between Lp spaces|journal=Ark. Mat.|volume=8|year=1969|pages=103–5|issue=2|bibcode = 1970ArM.....8..103E }}** Enflo, Per; 1969b: On a problem of Smirnov. Ark. Math., 8, pp. 107–109.** {{cite journal | last1 = Enflo | first1 = Per | year = 1970a | title = Uniform structures and square roots in topological groups I | url = | journal = Israel J. Math. | volume = 8 | issue = 3| pages = 230–252 | doi = 10.1007/BF02771560 }}** {{cite journal | last1 = Enflo | first1 = Per | year = 1970b | title = Uniform structures and square roots in topological groups II | url = | journal = Israel J. Math. | volume = 8 | issue = 3| pages = 253–272 | doi = 10.1007/BF02771561 }} 18. ^{{harvtxt|Kiselman|2010|p=1436}}: {{cite journal|title=Inverses and quotients of mappings between ordered sets|journal=Image and Vision Computing|volume=28|issue=10|year=2010|pages=1429–1442|url=|first=Christer O.|last=Kiselman|ref=harv|doi=10.1016/j.imavis.2009.06.014}} 19. ^1 {{cite web|title=Personal notes, in my own words|first=Per|last=Enflo|authorlink=Per Enflo|date=25 April 2011|accessdate=13 December 2011|ref=harv|publisher=perenflo.com|url=http://perenflo.com/sida9.html}} 20. ^Acknowledgement in {{cite book|last=Ribe|first=Martin|year=1972|title=On Spaces Which Are Not Supposed to be Locally Convex|format=doctoral thesis|location=Linköping|publisher=Högsk}} 21. ^{{cite journal|mr=2362689|last=Borwein|first=Jonathan M.|authorlink=Jonathan Borwein|title=Asplund decompositions of monotone operators|pages=19–25|journal=ESAIM Proc.|volume=17|year=2007|url=http://web.cs.dal.ca/~jborwein/decomps-paper.pdf|accessdate=13 December 2011|doi=10.1051/proc:071703|deadurl=yes|archiveurl=https://web.archive.org/web/20120415101530/http://web.cs.dal.ca/~jborwein/decomps-paper.pdf|archivedate=15 April 2012|df=}} 22. ^{{cite book|last1=Kalton|first1=Nigel J.|author1-link=Nigel Kalton|last2=Peck|first2=N. Tenney|last3=Roberts|first3=James W.| title = An F-space sampler| series = London Mathematical Society Lecture Note Series|volume=89| publisher = Cambridge University Press| location = Cambridge| year = 1984| pages = xii+240| isbn = 978-0-521-27585-9|mr=808777|ref=harv}} External links
6 : 1919 births|1970 deaths|Functional analysts|Mathematical analysts|20th-century mathematicians|Swedish mathematicians |
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