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Sigurður Helgason (mathematician)

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Sigurður Helgason (born 1927) is an Icelandic mathematician whose research has been devoted to the geometry and analysis on symmetric spaces. In particular he has 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.

Sigurður Helgason
Sigurður Helgason
Sigurður Helgason
Born1927 (1927) (age 92)
Akureyri, Iceland
OccupationMathematician
AwardsLeroy P. Steele Prize (1988)

He was born in Akureyri, Iceland. In 1954 he earned a PhD from Princeton University under Salomon Bochner. Since 1965, Helgason has been a professor of mathematics at the Massachusetts Institute of Technology.

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. This was followed by the 2008 book Geometric Analysis on Symmetric Spaces. On May 31, 1996 Helgason received an honorary doctorate from the Faculty of Science and Technology at Uppsala University, Sweden. [1]

He has been a fellow of the American Academy of Arts and Sciences since 1970. In 2012 he became a fellow of the American Mathematical Society.[2]

Selected worksEdit

ArticlesEdit

  • Helgason, S. (1954). "The derived algebra of a Banach algebra". Proc Natl Acad Sci U S A. 40 (10): 994–995. Bibcode:1954PNAS...40..994H. doi:10.1073/pnas.40.10.994. PMC 534208. PMID 16589593.
  • Helgason, Sigurður (1957). "Topologies of group algebras and a theorem of Littlewood". Trans. Amer. Math. Soc. 86 (2): 269–283. doi:10.1090/S0002-9947-1957-0095428-5. MR 0095428.
  • Helgason, Sigurður (1958). "Lacunary Fourier series on noncommutative groups". Proc. Amer. Math. Soc. 9 (5): 782–790. doi:10.1090/S0002-9939-1958-0100234-5. MR 0100234.
  • Helgason, Sigurður (1958). "On Riemannian curvature of homogeneous spaces". Proc. Amer. Math. Soc. 9 (6): 831–838. doi:10.1090/S0002-9939-1958-0108811-2. MR 0108811.
  • Helgason, S. (1962). "Some results on invariant theory". Bull. Amer. Math. Soc. 68 (4): 367–371. doi:10.1090/S0002-9904-1962-10812-X. MR 0166303.
  • Helgason, S. (1963). "Fundamental solutions to invariant differential operators on symmetric spaces". Bull. Amer. Math. Soc. 69 (6): 778–781. doi:10.1090/S0002-9904-1963-11029-0. MR 0156919.
  • Helgason, S. (1963). "Duality and Radon transforms for symmetric spaces". Bull. Amer. Math. Soc. 69 (6): 782–7881. doi:10.1090/S0002-9904-1963-11030-7. MR 0158408.
  • Helgason, Sigurður (1964). "A duality in integral geometry; some generalizations of the Radon transform". Bull. Amer. Math. Soc. 70 (4): 435–446. doi:10.1090/S0002-9904-1964-11147-2. MR 0166795.
  • Helgason, S. (1965). "Radon–Fourier transforms on symmetric spaces and related group representations". Bull. Amer. Math. Soc. 71 (5): 757–763. doi:10.1090/S0002-9904-1965-11380-5. MR 0179295.
  • with A. Korányi: Helgason, S.; Korányi, A. (1968). "A Fatou-type theorem for harmonic functions on symmetric spaces". Bull. Amer. Math. Soc. 74 (2): 258–263. doi:10.1090/S0002-9904-1968-11912-3. MR 0229179.
  • Helgason, Sigurður (1969). "Applications of the Radon transform to representations of semisimple Lie groups". Proc Natl Acad Sci U S A. 63 (3): 643–647. Bibcode:1969PNAS...63..643H. doi:10.1073/pnas.63.3.643. PMC 223499. PMID 16591772.
  • Helgason, Sigurður (1973). "Paley-Wiener theorems and surjectivity of invariant differential operators on symmetric spaces and Lie groups". Bull. Amer. Math. Soc. 79 (1): 129–132. doi:10.1090/S0002-9904-1973-13127-1. MR 0312158.
  • Helgason, Sigurður (1977). "Invariant differential equations and homogeneous manifolds" (PDF). Bull. Amer. Math. Soc. 83 (5): 751–774. doi:10.1090/S0002-9904-1977-14317-6. MR 0445235.

BooksEdit

ReferencesEdit

  1. ^ http://www.uu.se/en/about-uu/traditions/prizes/honorary-doctorates/
  2. ^ List of Fellows of the American Mathematical Society, retrieved 2013-01-21.
  3. ^ 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.
  4. ^ 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.
  5. ^ 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.
  6. ^ 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.

SourcesEdit

External linksEdit