the Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and Fredholm operators...

mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus...

Fredholm theory is a theory of integral equations. In the narrowest sense, Fredholm theory concerns itself with the solution of the Fredholm integral...

ways, as a theorem of linear algebra, a theorem of integral equations, or as a theorem on Fredholm operators. Part of the result states that a non-zero...

In mathematics, the Volterra integral equations are a special type of integral equations. They are divided into two groups referred to as the first and...

representations. An integral transform "maps" an equation from its original "domain" into another domain, in which manipulating and solving the equation may be much...

results from applying the resolvent formalism to solve Fredholm integral equations in Fredholm theory. The Liouville–Neumann series is defined as ϕ (...

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...

the theory of integral equations, where integral operators supply concrete examples of such operators. A typical Fredholm integral equation gives rise to...

range of factorings and rearrangements of the equation are possible. It is a Fredholm integral equation of the second kind, similar to those that arise...

the idea of the Fredholm integral equation and the Fredholm operator, and are one of the objects of study in Fredholm theory. Fredholm kernels are named...

mathematics, Fredholm operators are certain operators that arise in the Fredholm theory of integral equations. They are named in honour of Erik Ivar Fredholm. By...

in mathematics Fredholm determinant, in mathematics Fredholm integral equation, in mathematics Fredholm kernel, in mathematics Fredholm module, In noncommutative...

Erik Ivar Fredholm (7 April 1866 – 17 August 1927) was a Swedish mathematician whose work on integral equations and operator theory foreshadowed the theory...

decomposition method for nonhomogenous Fredholm integral equation of the second kind goes as follows: Given an integral equation of the form: u ( x ) = f ( x )...

\mathbf {H} _{\text{inc}}(r)} MFIE is often formulated to be a Fredholm integral equation of the second kind and is generally well-posed. Nevertheless,...

integral Vitali set, non-measurable set Henstock–Kurzweil integral Amenable group Banach–Tarski paradox Hausdorff paradox Fredholm equation Fredholm operator...

The Volterra equation may refer to the Volterra integral equation, an integral in the style of Fredholm theory. Product integral, an integral over an operator-valued...

{\displaystyle \nu (s)} is given by the unique solution to the Fredholm integral equation of the second kind, f ( x ) = − ν ( x ) 2 + ∫ ∂ D ν ( s ) ∂ G...

frequencies. Mathematically, the problem reduces to solving a Fredholm integral equation of the first kind with an ill-conditioned kernel. As a result...

variational problem is that C {\displaystyle C} must satisfy a Fredholm integral equation of the second kind C ( x ) = f ( x ) + ∫ K ( x , y ) C ( y ) d...

point of view the Lippmann–Schwinger equation in coordinate representation is an integral equation of Fredholm type. It can be solved by discretization...

each projection. Such an integral equation is known as a Fredholm integral equation, the study of which constitutes Fredholm theory. The primary use of...

increase the resolution without bound, we approach the kernel of the Fredholm integral equation of the 2nd kind, namely the Fourier operator that defines the...

This is a list of scientific equations named after people (eponymous equations). Contents A B C D E F G H I J K L M N O P R S T V W Y Z See also References...

and eigenfunctions ek, which are found solving the homogeneous Fredholm integral equation of the second kind ∫ a b K X ( s , t ) e k ( s ) d s = λ k e k...

expected the Riemann Hypothesis would be a consequence of Fredholm's work on integral equations with a symmetric kernel. At the time of Pólya's conversation...

other uses, the resolvent may be used to solve the inhomogeneous Fredholm integral equations; a commonly used approach is a series solution, the Liouville–Neumann...

find G, of course. See the articles on Green's functions and on Fredholm integral equations. It must be kept in mind that the above mathematics is purely...

it forms the Liouville-Neumann series that formally solves Fredholm integral equations. Suppose that T {\displaystyle T} is a bounded linear operator...