From Wikipedia, the free encyclopedia
Icelandic mathematician (1927–2023)
Sigurdur Helgason (
Icelandic : Sigurður Helgason ; 30 September 1927 – 3 December 2023) was an Icelandic
mathematician whose research has been devoted to the geometry and analysis on
symmetric spaces . In particular, he used new integral geometric methods to establish fundamental existence theorems for differential equations on symmetric spaces as well as some new results on the representations of their isometry groups. He also introduced a
Fourier transform on these spaces and proved the principal theorems for this
transform, the inversion formula, the
Plancherel theorem and the analog of the
Paley–Wiener theorem .
Biography
Sigurdur Helgason was born in
Akureyri , Iceland on 30 September 1927. In 1954, he earned a PhD from
Princeton University under
Salomon Bochner . Helgason became a professor of mathematics at the
Massachusetts Institute of Technology in 1965,
[1] and he retired from the faculty in 2014.
[2]
Helgason received the
Børge Jessen Diploma Award of the
Danish Mathematical Society in 1982, and the Grand Knight's Cross (Stórriddarakross ) of the Icelandic
Order of the Falcon in 1991.
[2]
[3] He was winner of the 1988
Leroy P. Steele Prize for Seminal Contributions for his books Groups and Geometric Analysis and Differential Geometry, Lie Groups and Symmetric Spaces .
[4] This was followed by the 2008 book Geometric Analysis on Symmetric Spaces . On 31 May 1996, Helgason received an
honorary doctorate from the Faculty of Science and Technology at
Uppsala University , Sweden.
[5]
Helgason was elected a member of the
Icelandic Academy of Sciences [
is ] in 1960, the
American Academy of Arts and Sciences in 1970,
[6] and the
Royal Danish Academy of Sciences and Letters in 1972.
[7]
[3] In 2013, he became a fellow of the
American Mathematical Society .
[8] He was made an honorary member of the
Icelandic Mathematical Society when he turned 70, and a symposium was held in his honor.
[3]
Helgason died on 3 December 2023, at the age of 96.
[9]
Selected works
Articles
Helgason, S. (1954).
"The derived algebra of a Banach algebra" .
Proceedings of the National Academy of Sciences of the United States of America . 40 (10): 994–995.
Bibcode :
1954PNAS...40..994H .
doi :
10.1073/pnas.40.10.994 .
PMC
534208 .
PMID
16589593 .
Helgason, Sigurdur (1957).
"Topologies of group algebras and a theorem of Littlewood" .
Transactions of the American Mathematical Society . 86 (2): 269–283.
doi :
10.1090/S0002-9947-1957-0095428-5 .
hdl :
1721.1/26691 .
MR
0095428 .
Helgason, Sigurdur (1958).
"Lacunary Fourier series on noncommutative groups" .
Proceedings of the American Mathematical Society . 9 (5): 782–790.
doi :
10.1090/S0002-9939-1958-0100234-5 .
MR
0100234 .
Helgason, Sigurdur (1958).
"On Riemannian curvature of homogeneous spaces" .
Proceedings of the American Mathematical Society . 9 (6): 831–838.
doi :
10.1090/S0002-9939-1958-0108811-2 .
MR
0108811 .
Helgason, S. (1962).
"Some results on invariant theory" .
Bulletin of the American Mathematical Society . 68 (4): 367–371.
doi :
10.1090/S0002-9904-1962-10812-X .
hdl :
1721.1/26682 .
MR
0166303 .
Helgason, S. (1963).
"Fundamental solutions to invariant differential operators on symmetric spaces" .
Bulletin of the American Mathematical Society . 69 (6): 778–781.
doi :
10.1090/S0002-9904-1963-11029-0 .
hdl :
1721.1/26683 .
MR
0156919 .
Helgason, S. (1963).
"Duality and Radon transforms for symmetric spaces" .
Bulletin of the American Mathematical Society . 69 (6): 782–7881.
doi :
10.1090/S0002-9904-1963-11030-7 .
hdl :
1721.1/26684 .
MR
0158408 .
Helgason, Sigurdur (1964).
"A duality in integral geometry; some generalizations of the Radon transform" .
Bulletin of the American Mathematical Society . 70 (4): 435–446.
doi :
10.1090/S0002-9904-1964-11147-2 .
hdl :
1721.1/26685 .
MR
0166795 .
Helgason, S. (1965).
"Radon–Fourier transforms on symmetric spaces and related group representations" .
Bulletin of the American Mathematical Society . 71 (5): 757–763.
doi :
10.1090/S0002-9904-1965-11380-5 .
hdl :
1721.1/26686 .
MR
0179295 .
Helgason, Sigurdur;
Korányi, Ádám (1968).
"A Fatou-type theorem for harmonic functions on symmetric spaces" .
Bulletin of the American Mathematical Society . 74 (2): 258–263.
doi :
10.1090/S0002-9904-1968-11912-3 .
hdl :
1721.1/26687 .
MR
0229179 .
Helgason, Sigurdur (1969).
"Applications of the Radon transform to representations of semisimple Lie groups" .
Proceedings of the National Academy of Sciences of the United States of America . 63 (3): 643–647.
Bibcode :
1969PNAS...63..643H .
doi :
10.1073/pnas.63.3.643 .
PMC
223499 .
PMID
16591772 .
Helgason, Sigurdur (1973). "Paley-Wiener theorems and surjectivity of invariant differential operators on symmetric spaces and Lie groups".
Bulletin of the American Mathematical Society . 79 (1): 129–132.
doi :
10.1090/S0002-9904-1973-13127-1 .
hdl :
1721.1/26688 .
MR
0312158 .
Helgason, Sigurdur (1977).
"Invariant differential equations and homogeneous manifolds" (PDF) .
Bulletin of the American Mathematical Society . 83 (5): 751–774.
doi :
10.1090/S0002-9904-1977-14317-6 .
MR
0445235 .
Books
References
^
"Sigurdur Helgason, Professor Emeritus of Mathematics, Dies at 96" , math.mit.edu ,
MIT Department of Mathematics , 6 December 2023, retrieved 2 April 2024
^
a
b
"Reports to the President For the Year Ended June 30, 2014, School of Science, Department of Mathematics: Retirements and Departures" (PDF) , web.mit.edu ,
MIT , retrieved 2 April 2024
^
a
b
c
"Íslenska stærðfræðafélagið: Heiðursfélagar" [Icelandic Mathematical Society: Honorary Members], stae.is (in Icelandic),
Icelandic Mathematical Society , retrieved 2 April 2024
^
"1988 Leroy P. Steele Prize winners" , ams.org ,
AMS , retrieved 2 April 2024
^
"Honorary doctorates - Uppsala University, Sweden" .
Uppsala University . 9 June 2023. Retrieved 2 April 2024 .
^
"Members: Professor Sigurður Helgason" , royalacademy.dk ,
Royal Danish Academy of Sciences and Letters , archived from
the original on 8 August 2022
^
"Member directory: Sigurdur Helgason" , amacad.org ,
AAA&S , retrieved 2 April 2024
^
"List of Fellows of the American Mathematical Society" , ams.org ,
AMS , retrieved 21 January 2013
^
"Andlát: Sigurður Helgason" . mbl.is (in Icelandic).
Morgunblaðið . 5 December 2023. Retrieved 10 December 2023 .
^
Auslander, Louis (1964).
"Review: Differential geometry and symmetric spaces , by S. Helgason" . Bull. Amer. Math. Soc . 70 (2): 227–229.
doi :
10.1090/S0002-9904-1964-11091-0 .
^
Kulkarni, Ravi S. (1980).
"Review: Differential geometry, Lie groups and symmetric spaces , by S. Helgason" . Bull. Amer. Math. Soc. (N.S.) . 2 (3): 468–476.
doi :
10.1090/S0273-0979-1980-14772-2 .
^
Howe, Roger (1989).
"Groups and geometric analysis. Integral geometry, invariant differential operators and spherical functions , by S. Helgason" . Bull. Amer. Math. Soc. (N.S.) . 20 (2): 252–256.
doi :
10.1090/S0273-0979-1989-15786-8 .
^ Rouvière, François (1995).
"Geometric analysis on symmetric spaces , by S. Helgason" . Bull. Amer. Math. Soc. (N.S.) . 32 (4): 441–446.
doi :
10.1090/S0273-0979-1995-00602-6 .
Sources
External links
International National Academics People Other