Approximating a Feller semigroup by using the Yosida approximation of the symbol of its generator (Q882832)

Let \(-q(x,D)\) be a pseudodifferential operator generating a Feller semigroup \(T_t\) and let \(T_t^v\) be generated by \(-q^v (x, D):= -\frac{v q}{v+ q}(x,D)\) for \(v>0\). Reasonable sufficient conditions are presented for \(T_t^v\) to converge to \(T_t\) uniformly as \(v\to\infty\). This approximation considerably simplifies the usual one \(-v q(x,D) (v+ q(x,D))^{-1}\).