• Abstract

In this paper, we establish global $C^2$ estimates to the Neumann problem for a class of fully nonlinear elliptic equations. As an application, we prove the existence and uniqueness of $k$-admissible solutions to the Neumann problems.

• General Summary

• Abstract

In various Hilbert spaces of analytic functions on the unit disk, we characterize when a function has optimal polynomial approximants given by truncations of a single power series or, equivalently, when the approximants stabilize. We also introduce a generalized notion of optimal approximant and use this to explicitly compute orthogonal projections of 1 onto certain shift invariant subspaces.

• General Summary