Resumen de Boundary differential relations for holomorphic functions on the disc

Miran Cerne, Matej Zajec

• The existence of solutions of boundary differential relations for holomorphic functions on the disc is considered. First we prove that for an arbitrary continuous positive function on the complex plane there exists a disc algebra function such that on . Assuming some smoothness, the existence result is also proved for a quite general differential relation , , where is a defining function for a family of Jordan curves in containing point 0 in its interior and is a bounded positive function on .