Weak pre-orthogonal adaptive Fourier decomposition in Bergman spaces of pseudoconvex domains

Abstract

We study a weak greedy type algorithm called the weak pre-orthogonal adaptive Fourier decomposition (WPOAFD) for the Bergman space on a bounded pseudoconvex domain Ω with smooth boundary. We show that any function can be approximated by linear combinations of kernel functions in weak greedy sense.