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We prove that operators of the form A=-a (x) ²^2, with suitable growth conditions on the coefficient a (x), generate analytic semigroups in L¹ (RN). In particular, we deduce generation results for the operator A: =- (1+|x|²) ^ ^2, 02. Moreover, we characterise the maximal domain of A in L¹ (RN).
Gregorio et al. (Mon,) studied this question.