Conformal Mappings and Boundary Value Problems.

摘要

Three principal areas of investigation are as follows; (1) Kernel functions and related areas, Results have been obtained on polynomial density in Ber's Spaces, Berman Spaces over multiply-connected domains, Total Positively and reproducing kernels, Szego kernels and the Riesz projection theorem and Metric on Annuli; (2) BVP (Boundary Value Problems), and IVP (Initial Value Problems), Study has been undertaken of transforming BVP into IVP. In particular, a method whereby a well-posed elliptic boundary-value problem of the Dirichlet type is transformed into a first-order non-linear equation governing the Green's function of an embedded problem is studied; and (3) Singularities, The study of smoothings of analytic singularities is discussed. In particular, generalized complete intersections and their spaces of deformations are analyzed.