Note on removable singularities

Removable Singularities In

Let A be a C*-algebra with identity and suppose A has real rank 0. Suppose a complex-valued function is holomorphic and bounded on the intersection of the open unit ball of A and the identity component of the set of invertible elements of A. We show that then the function has a holomorphic extension to the entire open unit ball of A. Further, we show that this does not hold when A = C(S), where...

On Removable Singularities for CRFunctions in Higher

Removable singularities for Hardy spaces

In this paper we study removable singularities for Hardy spaces of analytic functions on general domains. Two different definitions are given. For compact sets they turn out to be equal and moreover independent of the surrounding domain, as was proved by D. A. Hejhal. For non-compact sets the difference between the definitions is studied. A survey of the present knowledge is given, except for t...

Removable Singularities for Nonlinear Subequations

Let F be a fully nonlinear second-order partial differential subequation of degenerate elliptic type on a manifold X. We study the question: Which closed subsets E ⊂ X have the property that every F -subharmonic function (subsolution) on X−E, which is locally bounded across E, extends to an F -subharmonic function on X. We also study the related question for F -harmonic functions (solutions) wh...

Removable Singularities for Nonlinear Subequations

Let F be a fully nonlinear second-order partial differential subequation of degenerate elliptic type on a manifold X. We study the question: Which closed subsets E ⊂ X have the property that every F -subharmonic function (subsolution) on X − E, which is locally bounded across E, extends to an F -subharmonic function on X. We also study the related question for F harmonic functions (solutions) w...