differential operator

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Related to Differentiation operator: Linear differential operator

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 ?
A typical problem is to provide function theoretic characterizations when [phi] induces a bounded or compact products of differentiation operator and composition operator between two given spaces of analytic functions.
Motivated by [19, Theorem 3.3] which studies products of composition and differentiation on [H.sup.2], in Section 2 we calculate the exact value of Hilbert-Schmidt norms of products of composition and differentiation operators [C.sub.[phi]][D.sup.k], k [member of] N and D[C.sub.[phi]] on the Bergman space [A.sup.2.sub.[alpha]], [alpha] > -1 and the Hardy space [H.sup.2].
where [D.sub.N] is a discretization of the differentiation operator that is defined on the space of grid functions.
Let 0 < [alpha] < 1, and consider the fractional differentiation operators of even and odd parities, defined for tempered distributions [mathematical expression not reproducible].