The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman

Integral Formulas and the Ohsawa-takegoshi Extension Theorem

We construct a semiexplicit integral representation of the canonical solution to the ∂̄-equation with respect to a plurisubharmonic weight function in a pseudoconvex domain. The construction is based on a construction related to the Ohsawa-Takegoshi extension theorem combined with a method to construct weighted integral representations due to M Andersson.

An extension theorem for finite positive measures on surfaces of finite‎ ‎dimensional unit balls in Hilbert spaces

A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kante...

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

MATRIX VALUATION PSEUDO RING (MVPR) AND AN EXTENSION THEOREM OF MATRIX VALUATION

Let R be a ring and V be a matrix valuation on R. It is shown that, there exists a correspondence between matrix valuations on R and some special subsets ?(MVPR) of the set of all square matrices over R, analogous to the correspondence between invariant valuation rings and abelian valuation functions on a division ring. Furthermore, based on Malcolmson’s localization, an alternative proof for t...

An extension of the Wedderburn-Artin Theorem

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.