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...

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

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

{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 a...

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

{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...

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...

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

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

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...

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...

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

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

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

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

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

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

In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that the vector field alters...

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

notation. Thus, in these cases, it may be preferable to use the Euler differential operator notation with D i {\displaystyle D_{i}} as the partial derivative...

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

\cdots .} The Zernike polynomials are eigenfunctions of the Zernike differential operator, in modern formulation L [ f ] = ∇ 2 f − ( r ⋅ ∇ ) 2 f − 2 r ⋅ ∇...