Functions of a quaternion variable which are gradients of real-valued functions.
Functions satisfying a discrete mean value property.
Fundamental solutions of differential operators on homogeneous manifolds of negative curvature and related Riesz transforms
Fundamental solutions of the complex Monge-Ampère equation
We prove that any positive function on ℂℙ¹ which is constant outside a countable -set is the order function of a fundamental solution of the complex Monge-Ampère equation on the unit ball in ℂ² with a singularity at the origin.
Funktionen, deren Logarithmus darstellbar ist als Differenz subharmonischer Funktionen
Further pseudodifferential operators generating Feller semigroups and Dirichlet forms.
We prove for a large class of symmetric pseudo differential operators that they generate a Feller semigroup and therefore a Dirichlet form. Our construction uses the Yoshida-Hille-Ray Theorem and a priori estimates in anisotropic Sobolev spaces. Using these a priori estimates it is possible to obtain further information about the stochastic process associated with the Dirichlet form under consideration.