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Linear differential filters, i.e., filters in which the filtered function f̄ and the original function f are connected by a linear differential equation, are studied on a general basis concerning the elliptic operators of second order. In addition, a particular example of a parabolic filter depending on space and extended to past times is given, and its interest in the context of the large eddy simulation of turbulence is discussed.
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Massimo Germano (1986) studied this question.
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