Erik Ivar Fredholm (7 April 1866 – 17 August 1927) was a Swedish

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, structure, space, models, and change. History On ...

whose work on

integral equation In mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: f(x_1,x_2,x_3,...,x_n ; u(x_1,x_2,x_3,...,x_n) ...

s and

operator theory In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators ...

foreshadowed the theory of

Hilbert space In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise natural ...

Biography

Fredholm was born in Stockholm in 1866. He obtained his PhD 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 during ...

in 1898, under the supervision of

Gösta Mittag-Leffler Magnus Gustaf "Gösta" Mittag-Leffler (16 March 1846 – 7 July 1927) was a Swedish mathematician. His mathematical contributions are connected chiefly with the theory of functions, which today is called complex analysis. Biography Mittag-Leffl ...

. He was ''docent'' at

Stockholm University Stockholm University ( sv, Stockholms universitet) is a public research university in Stockholm, Sweden, founded as a college in 1878, with university status since 1960. With over 33,000 students at four different faculties: law, humanities, ...

from 1898 to 1906 and professor from 1906 until his death. In 1914 he was elected a member of the

Royal Swedish Academy of Sciences The Royal Swedish Academy of Sciences ( sv, Kungliga Vetenskapsakademien) is one of the royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special responsibility for prom ...

. Beside his academic career he was recruited to the

Swedish Social Insurance Agency The Swedish Social Insurance Agency ( sv, Försäkringskassan, ) is a government agency that administers social insurance in Sweden. Responsibilities Among other the agency is responsible for administering the following benefits. * Immigrant ...

when it was founded in 1902. He later served as an actuary at the insurance company Skandia (1904-1927), where his Fredholm equation was used to calculate buyback-prices. From 1911, he was married to Agnes Maria Liljeblad, the secretary of Mittag-Leffler.

Mathematical work

In , Fredholm introduced and analysed a class of integral equations now called Fredholm equations. His

analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...

included the construction of

Fredholm determinant In mathematics, the Fredholm determinant is a complex-valued function which generalizes the determinant of a finite dimensional linear operator. It is defined for bounded operators on a Hilbert space which differ from the identity operator by a tra ...

s, and the proof of the

Fredholm theorem In mathematics, Fredholm's theorems are a set of celebrated results of Ivar Fredholm in the Fredholm theory of integral equations. There are several closely related theorems, which may be stated in terms of integral equations, in terms of linear a ...

Honours

Fredholm was a member of the

Finnish Society of Sciences and Letters The Finnish Society of Sciences and Letters is a Finnish academy for natural sciences, social sciences and humanities. It is known in Latin as Societas Scientiarum Fennica, in Swedish as Finska Vetenskaps-Societeten, and in Finnish as Suomen Ti ...

and of the

Accademia dei Lincei The Accademia dei Lincei (; literally the " Academy of the Lynx-Eyed", but anglicised as the Lincean Academy) is one of the oldest and most prestigious European scientific institutions, located at the Palazzo Corsini on the Via della Lungara in R ...

; he was awarded the

Poncelet Prize The Poncelet Prize (french: Prix Poncelet) is awarded by the French Academy of Sciences. The prize was established in 1868 by the widow of General Jean-Victor Poncelet for the advancement of the sciences. It was in the amount of 2,000 francs (as of ...

for 1908. The lunar crater '' Fredholm'' is named after him as is the asteroid 21659 Fredholm.

Publications

* * *

Notes

References

* * * * *

External links

* * * Evans M. Harrell II,
A Short History of Operator Theory
' (2004) 1866 births 1927 deaths 19th-century Swedish mathematicians 20th-century Swedish mathematicians {{Sweden-mathematician-stub