# differential operator

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## differential operator

[‚dif·ə′ren·chəl ′äp·ə‚rād·ər]
(mathematics)
An operator on a space of functions which maps a function ƒ into a linear combination of higher-order derivatives of ƒ.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
It is interesting to note that several integral and differential operator follows as a special case of [[D.sub.[lambda].sup.[delta]](f * g)(z), here we list few of them.
Precisely, the linear algebra step is performed modulo several primes p, and the results (differential operators modulo p) are recombined over Q via rational reconstruction based on an effective version of the Chinese remainder theorem.
Proposition 2 (Marchenko) Let [[alpha].sub.n] > [[lambda].sub.n] and An be two sequences of real numbers such that [absolute value of [[lambda].sub.n]] is strictly increasing; then there exists a unique continuous function q on [0, [infinity] and a real constant h such that the differential operator in (4) has spectral data [{[[alpha].sub.n], [[lambda].sub.n]}.sub.n[greater than or equal to] 0] if and only if the function [PHI](x) := [summation over (k [greater than or equal to] 0)] 1-cos(x [[lambda].sub.k)]/[[alpha].sup.2.sub.k] [[lambda].sup.2.sub.k] is thrice continuously differentiable and [PHI]'(0+) = 1.
Let the Hilbert space H be given by (3.1) and let A be the self-adjoint differential operator in H defined in (3.3).
In this paper we consider, for [alpha] > 0, the following system of partial differential operators
We now introduce various differential operators associated to the Riemannian manifold (X, g).
In the fourth volume of his series on invariant differential operators, Dobrev begins with aspects of the AdS/CFT correspondence, or more generally relativistic and non-relativistic holography.
It is obvious that the second-order differential equations can always be considered in a factorization form as a product of a pair of linear differential operators (14) and (15).
The difference between the original dressing method and the generalized dressing method lies in the differential operators [M.sub.1] and [M.sub.2] which satisfied the relation
where [alpha],[beta], [gamma] [member of] (0,1], [R.sup.i], [N.sup.i], i = 1,2,3, denote linear differential operators and nonlinear differential operators, respectively, and [g.sup.i] (x, t) are the source terms.
Rozenbljum, "Distribution of the discrete spectrum of singular differential operators," Doklady Akademii Nauk SSSR, vol.
We now try to decompose the differential operator [L.sup.2.sub.[alpha]] into differential operators [L.sub.A(r)] and [L.sub.B(r)] of first order such that

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