In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first...

mathematical analysis a pseudo-differential operator is an extension of the concept of differential operator. Pseudo-differential operators are used extensively...

In differential geometry there are a number of second-order, linear, elliptic differential operators bearing the name Laplacian. This article provides...

Del, or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by the nabla...

the theory of partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined by the...

(abbreviated, in this article, as linear operator or, simply, operator) is a linear combination of basic differential operators, with differentiable functions as...

{\displaystyle \nabla } is taken as a vector differential operator del. Such notation involving operators is common in physics and algebra. Expanded in...

In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean space...

In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean...

{n}{k}}={\tbinom {n}{n-k}}} . The naturalness of the star operator means it can play a role in differential geometry, when applied to the cotangent bundle of...

mathematics, differential algebra is, broadly speaking, the area of mathematics consisting in the study of differential equations and differential operators as...

line is in one sense the spectral theory of differentiation as a differential operator. But for that to cover the phenomena one has already to deal with...

{He} _{\lambda }(x)} may be understood as eigenfunctions of the differential operator L [ u ] {\displaystyle L[u]} . This eigenvalue problem is called...

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

correspond to the eigenvalues and eigenfunctions of a Hermitian differential operator in an appropriate Hilbert space of functions with inner product...

In mathematics and theoretical physics, an invariant differential operator is a kind of mathematical map from some objects to an object of similar type...

particular kind of differential equation under consideration. There is a well-developed theory for linear differential operators, due to Lars Gårding...

d'Alembert operator (denoted by a box: ◻ {\displaystyle \Box } ), also called the d'Alembertian, wave operator, box operator or sometimes quabla operator (cf...

in the context of differential equations defined by a vector valued function Rn to Rm, the Fréchet derivative A is a linear operator on R considered as...

A vector operator is a differential operator used in vector calculus. Vector operators include: Gradient is a vector operator that operates on a scalar...

problems, in the linear case, involves the eigenfunctions of a differential operator. To be useful in applications, a boundary value problem should be...

take many forms. For example, the linear transformation could be a differential operator like d d x {\displaystyle {\tfrac {d}{dx}}} , in which case the...

potential field V. Differential operators are an important class of unbounded operators. The structure of self-adjoint operators on infinite-dimensional...

In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives...

1832. Oliver Heaviside introduced the practical use of fractional differential operators in electrical transmission line analysis circa 1890. The theory...

form of a linear homogeneous differential equation is L ( y ) = 0 {\displaystyle L(y)=0} where L is a differential operator, a sum of derivatives (defining...

an upside-down triangle and pronounced "del", denotes the vector differential operator. When a coordinate system is used in which the basis vectors are...

a Dirac operator is a first-order differential operator that is a formal square root, or half-iterate, of a second-order differential operator such as...

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

representation theory, differential geometry, quantum statistical mechanics, quantum information, and quantum field theory. Operator algebras can be used...