Consistency of Regularization for Scalar Fields

Throughout this note, m0 > 0, and P : R → R is a polynomial which is bounded from below. If Σ̂ is a closed Riemannian surface, then D(Σ̂) and D′(Σ̂) denote the spaces of smooth and generalized functions (or distributions) on Σ̂, respectively, and a function f is identified with the distribution fdA, where dA is the Riemannian area form. The pairing of a… (More)