Sigurdur Helgason (mathematician)

Sigurdur Helgason
Sigurdur Helgason
Born	1927 (1927) (age 87) Akureyri, Iceland
Occupation	Icelandic mathematician

Sigurdur Helgason (born 1927) is an Icelandic-American 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. 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. 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.^[1]

Selected works

Articles

• 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, Sigur{\Dbar}ur (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, Sigur{\Dbar}ur (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, Sigur{\Dbar}ur (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, Sigurdur (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, Sigurdur (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, Sigurdur (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, Sigurdur (1977). "Invariant differential equations and homogeneous manifolds". Bull. Amer. Math. Soc. 83 (5): 751–774. doi:10.1090/S0002-9904-1977-14317-6. MR 0445235. 

Books

• Differential geometry and symmetric spaces. Academic Press 1962,^[2] AMS 2001
• Analysis on Lie groups and homogeneous spaces. AMS 1972
• Differential geometry, Lie groups and symmetric spaces. Academic Press 1978,^[3] 7th edn. 1995
• The Radon Transform. Birkhäuser, 1980, 2nd edn. 1999
• Topics in harmonic analysis on homogeneous spaces. Birkhäuser 1981
• Groups and geometric analysis: integral geometry, invariant differential operators and spherical functions. Academic Press 1984,^[4] AMS 1994
• Geometric analysis on symmetric spaces. AMS 1994,^[5] 2nd. edn. 2008

References

Sources

• "Curriculum vitae". Massachusetts Institute of Technology. 2005. 
• "Sigurdur Helgason". Massachusetts Institute of Technology. 

External links

• Sigurdur Helgason at the Mathematics Genealogy Project
• Sigurdur Helgason - Publications - MIT Mathematics