In mathematical analysis, an integral linear operator is a linear operator T given by integration; i.e., ( T f ) ( x ) = ∫ f ( y ) K ( x , y ) d y {\displaystyle...

the integral symbol Integral linear operators, which are linear operators induced by bilinear forms involving integrals Integral transforms, which are...

built from them are called differential operators, integral operators or integro-differential operators. Operator is also used for denoting the symbol of...

mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may...

integral transforms vary widely, they have some properties in common. For example, every integral transform is a linear operator, since the integral is...

In functional analysis, a branch of mathematics, a compact operator is a linear operator T : X → Y {\displaystyle T:X\to Y} , where X , Y {\displaystyle...

a linear endomorphism. Sometimes the term linear operator refers to this case, but the term "linear operator" can have different meanings for different...

integral equations are a special type of integral equations. They are divided into two groups referred to as the first and the second kind. A linear Volterra...

of functional analysis and operator theory, the Volterra operator, named after Vito Volterra, is a bounded linear operator on the space L2[0,1] of complex-valued...

In functional analysis and operator theory, a bounded linear operator is a linear transformation L : X → Y {\displaystyle L:X\to Y} between topological...

to closure of graphs Continuous linear operator – Function between topological vector spaces Densely defined operator – Function that is defined almost...

I^{m}(u))=0} where I i ( u ) {\displaystyle I^{i}(u)} is an integral operator acting on u. Hence, integral equations may be viewed as the analog to differential...

g {\displaystyle f*g} , denoting the operator with the symbol ∗ {\displaystyle *} . It is defined as the integral of the product of the two functions after...

second-order differential operator, the Laplace operator maps Ck functions to Ck−2 functions for k ≥ 2. It is a linear operator Δ : Ck(Rn) → Ck−2(Rn), or...

integral operators. Every bounded operator with a finite-dimensional range (these are called operators of finite rank) is a Hilbert–Schmidt operator....

means that the solutions may be expressed in terms of integrals. This is also true for a linear equation of order one, with non-constant coefficients...

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

_{a}^{b}g} to express the linearity of the integral, a property shared by the Riemann integral and all generalizations thereof. Integrals appear in many practical...

In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features...

(continuous) linear combination in the form of an integral over the parameter ξ. But this integral was in the form of a Fourier integral. The next step...

integration: the linear transformation defined by the Riemann integral I ( f ) = ∫ a b f ( x ) d x {\displaystyle I(f)=\int _{a}^{b}f(x)\,dx} is a linear functional...

direct integrals of von Neumann algebras. The concept was introduced in 1949 by John von Neumann in one of the papers in the series On Rings of Operators. One...

self-adjoint operator on a complex vector space V with inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is a linear map A (from V...

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

&{\mbox{otherwise}}.\end{matrix}}\right.} The Volterra operator is the corresponding integral operator T on the Hilbert space L2(0,1) given by T f ( x ) =...

logic Operator (mathematics), mapping that acts on elements of a space to produce elements of another space, e.g.: Linear operator Differential operator Integral...

insights about an improved forward map. When operator F {\displaystyle F} is linear, the inverse problem is linear. Otherwise, that is most often, the inverse...

α, and is therefore linear. The concept of linearity can be extended to linear operators. Important examples of linear operators include the derivative...

In linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented...

with understanding the theory of pseudo-differential operators. Consider a linear differential operator with constant coefficients, P ( D ) := ∑ α a α D α...