Sigurdur Helgason (born 30 September 1927; Icelandic: ''Sigurður'') is an Icelandic

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

whose research has been devoted to the geometry and analysis on

symmetric spaces In mathematics, a symmetric space is a Riemannian manifold (or more generally, a pseudo-Riemannian manifold) whose group of symmetries contains an inversion symmetry about every point. This can be studied with the tools of Riemannian geometry, ...

. 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 A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...

on these spaces and proved the principal theorems for this transform, the inversion formula, the

Plancherel theorem In mathematics, the Plancherel theorem (sometimes called the Parseval–Plancherel identity) is a result in harmonic analysis, proven by Michel Plancherel in 1910. It states that the integral of a function's squared modulus is equal to the integr ...

and the analog of the

Paley–Wiener theorem In mathematics, a Paley–Wiener theorem is any theorem that relates decay properties of a function or distribution at infinity with analyticity of its Fourier transform. The theorem is named for Raymond Paley (1907–1933) and Norbert Wiener (189 ...

. He was born in

Akureyri Akureyri (, locally ) is a town in northern Iceland. It is Iceland's fifth-largest municipality, after Reykjavík, Hafnarfjörður, Reykjanesbær and Kópavogur, and the largest town outside Iceland's more populated southwest corner. Nickname ...

, Iceland. In 1954, he earned a PhD from

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the n ...

under

Salomon Bochner Salomon Bochner (20 August 1899 – 2 May 1982) was an Austrian mathematician, known for work in mathematical analysis, probability theory and differential geometry. Life He was born into a Jewish family in Podgórze (near Kraków), then Au ...

. Since 1965, Helgason has been a professor of mathematics at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private Land-grant university, land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern t ...

. He was winner of the 1988

Leroy P. Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have ...

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 An honorary degree is an academic degree for which a university (or other degree-awarding institution) has waived all of the usual requirements. It is also known by the Latin phrases ''honoris causa'' ("for the sake of the honour") or '' ad ho ...

from the Faculty of Science and Technology at

Uppsala University Uppsala University ( sv, Uppsala universitet) is a public research university in Uppsala, Sweden. Founded in 1477, it is the oldest university in Sweden and the Nordic countries still in operation. The university rose to significance durin ...

, Sweden. He has been a fellow of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, ...

since 1970. In 2012, he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings ...

Selected works

Articles

* * * * * * * * * * * * *

Books

*''Differential geometry and symmetric spaces''. Academic Press 1962, AMS 2001 *''Analysis on

Lie group In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the addit ...

s and

homogeneous space In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group ''G'' is a non-empty manifold or topological space ''X'' on which ''G'' acts transitively. The elements of ...

s''. AMS 1972 *'' Differential geometry, Lie groups and

symmetric space In mathematics, a symmetric space is a Riemannian manifold (or more generally, a pseudo-Riemannian manifold) whose group of symmetries contains an inversion symmetry about every point. This can be studied with the tools of Riemannian geometry, ...

s''. Academic Press 1978, 7th edn. 1995 *''The

Radon Transform In mathematics, the Radon transform is the integral transform which takes a function ''f'' defined on the plane to a function ''Rf'' defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the ...

''. Birkhäuser, 1980, 2nd edn. 1999 *''Topics in

harmonic analysis Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an e ...

on homogeneous spaces''. Birkhäuser 1981 *''Groups and

geometric analysis Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology In mathem ...

integral geometry In mathematics, integral geometry is the theory of measures on a geometrical space invariant under the symmetry group of that space. In more recent times, the meaning has been broadened to include a view of invariant (or equivariant) transformat ...

, invariant differential operators and spherical functions''. Academic Press 1984, AMS 1994 *''Geometric analysis on symmetric spaces''. AMS 1994, 2nd. edn. 2008

References

Sources

* *

External links

*
Sigurdur Helgason – Publications – MIT Mathematics
{{DEFAULTSORT:Helgason, Sigurdur 1927 births Living people Sigurdur Helgason Differential geometers Massachusetts Institute of Technology School of Science faculty Fellows of the American Mathematical Society 20th-century mathematicians 21st-century mathematicians Sigurdur Helgason People from Akureyri Princeton University alumni