Erik Ivar Fredholm
Encyclopedia
Erik Ivar Fredholm was a Swedish mathematician
who established the modern theory of integral equation
s. His 1903 paper in Acta Mathematica is considered to be one of the major landmarks in the establishment of operator theory
.
The lunar crater Fredholm
is named after him.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who established the modern theory of integral equation
Integral equation
In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way...
s. His 1903 paper in Acta Mathematica is considered to be one of the major landmarks in the establishment of operator theory
Operator theory
In mathematics, operator theory is the branch of functional analysis that focuses on bounded linear operators, but which includes closed operators and nonlinear operators.Operator theory also includes the study of algebras of operators....
.
The lunar crater Fredholm
Fredholm (crater)
Fredholm is a small lunar impact crater that is located in the rugged ground to the west of the Mare Crisium. It lies mid-way between the prominent craters Macrobius to the north and Proclus almost due south....
is named after him.
List of publications
- E.I. Fredholm, "Sur une classe d'equations fonctionnelles", Acta MathematicaActa MathematicaActa Mathematica is a journal publishing original research papers in all fields of mathematics. The journal was founded by Gösta Mittag-Leffler in 1882 and is published by Institut Mittag-Leffler, a research institute for mathematics belonging to the Royal Swedish Academy of Sciences...
, 27 (1903) pp. 365–390.
See also
- Analytic Fredholm theoremAnalytic Fredholm theoremIn mathematics, the analytic Fredholm theorem is a result concerning the existence of bounded inverses for a family of bounded linear operators on a Hilbert space. It is the basis of two classical and important theorems, the Fredholm alternative and the Hilbert–Schmidt theorem...
- Fredholm alternativeFredholm alternativeIn mathematics, the Fredholm alternative, named after Ivar Fredholm, is one of Fredholm's theorems and is a result in Fredholm theory. It may be expressed in several ways, as a theorem of linear algebra, a theorem of integral equations, or as a theorem on Fredholm operators...
- Fredholm determinantFredholm determinantIn mathematics, the Fredholm determinant is a complex-valued function which generalizes the determinant of a matrix. It is defined for bounded operators on a Hilbert space which differ from the identity operator by a trace-class operator...
- Fredholm equation
- Fredholm kernelFredholm kernelIn mathematics, a Fredholm kernel is a certain type of a kernel on a Banach space, associated with nuclear operators on the Banach space. They are an abstraction of the idea of the Fredholm integral equation and the Fredholm operator, and are one of the objects of study in Fredholm theory....
- Fredholm moduleFredholm moduleIn noncommutative geometry, a Fredholm module is a mathematical structure used to quantize the differential calculus. Such a module is, up to trivial changes, the same as the abstract elliptic operator introduced by .-Definition:...
- Fredholm operatorFredholm operatorIn mathematics, a Fredholm operator is an operator that arises in the Fredholm theory of integral equations. It is named in honour of Erik Ivar Fredholm....
- Fredholm theoryFredholm theoryIn mathematics, Fredholm theory is a theory of integral equations. In the narrowest sense, Fredholm theory concerns itself with the solution of the Fredholm integral equation. In a broader sense, the abstract structure of Fredholm's theory is given in terms of the spectral theory of Fredholm...
External links
- Evans M. Harrell II, A Short History of Operator Theory (2004)