differential operator

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differential operator

n
(Mathematics) any operator involving differentiation, such as the mathematical operator del ∇, used in vector analysis, where ∇ = i∂/∂x + j∂/∂y+ k∂/∂z, i, j, and k being unit vectors and ∂/∂x, ∂/∂y, and ∂/∂z the partial derivatives of a function in x, y, and z
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Classes of analytic functions of complex order involving a Family of generalized differential operators *
Self-adjoint differential operators associated with self-adjoint differential expressions.
In a volume based on courses he taught at Saint-Petersburg (Russia) and Rennes (France) Universities, Yafaev describes applications of scattering theory methods to differential operators, primarily the Schrodinger operator.
If the first N terms of a power series S [member of] Q[[t]] are available, one can search for a differential equation satisfied by S at precision N, that is, for an element L in the Weyl algebra Q[t]<[D.sub.t]> of differential operators in the derivation [D.sub.t] = d/dt with polynomial coefficients in t, such that
Nairnark, Linear Differential Operators, Part II, Ungar, New York, 1969.
NAIMARK, Linear Differential Operators II, Frederick Ungar, New York, 1968.
We provide a generalization of Calderon's reproducing formula associated with partial differential operators on the half-plane involving finite Borel measures.
These techniques, which involve the theory of overdetermined linear partial differential equations (see [6] and [9]) and harmonic analysis on homogeneous spaces of compact Lie groups, are supplemented here by new results about complexes of differential operators on symmetric spaces (see [sections]1) and an analysis of the Lichnerowicz Laplacian [delta] acting on symmetric 2-forms, in relation both to these complexes and to representation theory of the group G.
Invariant Differential Operators; Volume 4: AdS/CFT, (Super-)Virasoro, Affine (Super-)Algebras
Moreover, the second-order differential equation also can be considered as a product of two first-order differential operators and the spinor wave function related to the differential equation that is expressed in terms of Rodrigues representations related to the orthogonal polynomials.

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