John T. Anderson

Polynomial approximation on three-dimensional real-analytic submanifolds of ⁿ

It was once conjectured that if A is a uniform algebra on its maximal ideal space X and if each point of X is a peak point for A, then A = C(X). This peak point conjecture was disproved by Brian Cole in 1968. However, it was recently shown by Anderson and Izzo that the peak point conjecture does hold for uniform algebras generated by smooth functions on smooth twomanifolds with boundary. Although the corresponding assertion for smooth three-manifolds is false, we establish a peak point theorem for real-analytic three-manifolds with boundary.

A Peak Point Theorem for Uniform Algebras on Real-Analytic Varieties

It was once conjectured that if

Approximation Problems on the Unit Sphere in C2

A

Recovering H p functions from partial boundary data

A is a uniform algebra on its maximal ideal space

A Peak Point Theorem for Uniform Algebras Generated by Smooth Functions on Two-Manifolds

X

L^p

X, and if each point of