ANALYTICITY OF SEMIGROUPS GENERATED BY SECOND-ORDER DIFFERENTIAL OPERATORS ON WEIGHTED L2-SPACES

Abstract

We study a family of second-order differential operators with unbounded coefficients (and possibly singular). We show that such operators generate analytic semigroups on L2((0, w), ρ2dx), 0 < w ≤ ∞, where dx denotes the Lebesgue measure. The choice of the weight ρ2 will depend on the form of the considered operator and on its coefficients.