Category Archives: Diffusions on manifolds

In this lecture, we consider a diffusion operator L which is essentially self-adjoint. Its Friedrichs extension is still denoted by L. The fact that we are now dealing with a non negative self-adjoint operator allows us to use spectral theory … Continue reading →

The goal of the next few lectures will be to introduce the semigroup generated by a diffusion operator. The construction of the semigroup is non trivial because diffusion operators are unbounded operators. We consider a diffusion operator where and are … Continue reading →

Definition: A differential operator on , is called a diffusion operator if it can be written where and are continuous functions on and if for every , the matrix is a symmetric and nonnegative matrix. If for every the matrix is … Continue reading →