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Given the Sobolev bilinear form (f, g)S =>u0, fg< + >u1, f " g "<, with u0 and u1 linear functionals, a characterization of the linear second–order differential operators with polynomial coefficients, symmetric with respect to (⋅, ⋅)S in terms of u0 and u1 is obtained. In particular, several interesting functionals u0 and u1 are considered, recovering as particular...
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