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...
22 KB (3,650 words) - 11:48, 7 November 2023
mathematical analysis a pseudo-differential operator is an extension of the concept of differential operator. Pseudo-differential operators are used extensively...
10 KB (1,402 words) - 01:53, 11 July 2023
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean...
27 KB (4,069 words) - 15:23, 12 June 2024
the theory of partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined by the...
10 KB (1,505 words) - 04:43, 24 March 2024
Curl (mathematics) (redirect from Curl (differential operator))
Cartesian coordinates if ∇ is taken as a vector differential operator del. Such notation involving operators is common in physics and algebra. Expanded in...
34 KB (4,932 words) - 13:45, 19 May 2024
Del (redirect from Vector differential operator)
Del, or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by the nabla...
21 KB (3,846 words) - 05:41, 26 May 2024
are built from them are called differential operators, integral operators or integro-differential operators. Operator is also used for denoting the symbol...
13 KB (1,857 words) - 21:52, 8 May 2024
(abbreviated, in this article, as linear operator or, simply, operator) is a linear combination of basic differential operators, with differentiable functions as...
30 KB (4,757 words) - 09:44, 12 April 2024
In mathematics and theoretical physics, an invariant differential operator is a kind of mathematical map from some objects to an object of similar type...
9 KB (1,324 words) - 08:07, 9 February 2024
In differential geometry there are a number of second-order, linear, elliptic differential operators bearing the name Laplacian. This article provides...
8 KB (1,099 words) - 08:46, 13 May 2024
In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean space...
20 KB (3,344 words) - 06:20, 21 June 2024
Sturm–Liouville theory (redirect from Sturm-Liouville differential operator)
correspond to the eigenvalues and eigenfunctions of a Hermitian differential operator in an appropriate Hilbert space of functions with inner product...
30 KB (4,692 words) - 23:36, 6 June 2024
Spectral theory (redirect from Spectral theory of differential operators)
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...
32 KB (4,668 words) - 11:23, 22 May 2024
potential field V. Differential operators are an important class of unbounded operators. The structure of self-adjoint operators on infinite-dimensional...
48 KB (8,049 words) - 16:06, 25 May 2024
Hermite polynomials (redirect from Hermite differential equation)
{He} _{\lambda }(x)} may be understood as eigenfunctions of the differential operator L [ u ] {\displaystyle L[u]} . This eigenvalue problem is called...
56 KB (10,011 words) - 16:24, 12 June 2024
particular kind of differential equation under consideration. There is a well-developed theory for linear differential operators, due to Lars Gårding...
9 KB (1,251 words) - 06:26, 21 May 2024
mathematics, differential algebra is, broadly speaking, the area of mathematics consisting in the study of differential equations and differential operators as...
61 KB (7,867 words) - 15:43, 25 May 2024
Atiyah–Singer index theorem (redirect from Symbol of an elliptic operator)
applications to theoretical physics. The index problem for elliptic differential operators was posed by Israel Gel'fand. He noticed the homotopy invariance...
53 KB (7,529 words) - 04:31, 30 May 2024
In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function...
50 KB (6,872 words) - 16:27, 20 June 2024
A vector operator is a differential operator used in vector calculus. Vector operators include the gradient, divergence, and curl: Gradient is a vector...
2 KB (215 words) - 02:19, 4 January 2024
mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may...
12 KB (1,543 words) - 22:04, 24 May 2024
pseudo-differential equations use pseudo-differential operators instead of differential operators. A differential algebraic equation (DAE) is a differential...
30 KB (3,650 words) - 01:59, 4 May 2024
quantum mechanics, operator theory and harmonic analysis on semisimple Lie groups. Spectral theory for second order ordinary differential equations on a compact...
63 KB (9,370 words) - 02:43, 14 December 2023
Gradient (redirect from Gradient Operator)
an upside-down triangle and pronounced "del", denotes the vector differential operator. When a coordinate system is used in which the basis vectors are...
37 KB (5,672 words) - 21:15, 23 June 2024
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...
101 KB (13,536 words) - 07:44, 25 June 2024
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...
23 KB (3,555 words) - 03:28, 7 April 2024
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...
9 KB (1,251 words) - 18:47, 29 April 2024
operator is the operator associated with the linear momentum. The momentum operator is, in the position representation, an example of a differential operator...
13 KB (2,031 words) - 23:14, 12 June 2024
{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...
42 KB (6,824 words) - 21:45, 23 June 2024
Green's function (category Differential equations)
Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary...
38 KB (5,120 words) - 10:47, 20 June 2024