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

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

Cartesian coordinates if ∇ is taken as a vector differential operator del. Such notation involving operators is common in physics and algebra. Expanded in...

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

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

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

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

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

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

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...

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

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

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

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

applications to theoretical physics. The index problem for elliptic differential operators was posed by Israel Gel'fand. He noticed the homotopy invariance...

In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function...

A vector operator is a differential operator used in vector calculus. Vector operators include the gradient, divergence, and curl: Gradient is a vector...

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

pseudo-differential equations use pseudo-differential operators instead of differential operators. A differential algebraic equation (DAE) is a differential...

{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...

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

quantum mechanics, operator theory and harmonic analysis on semisimple Lie groups. Spectral theory for second order ordinary differential equations on a compact...

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...

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 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...

operator is the operator associated with the linear momentum. The momentum operator is, in the position representation, an example of a differential operator...

Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary...