Abstract:
The Dirichlet problem in the disk is solved two ways. First, we use the real
and imaginary part of z
n
together with Fourier series. A Fourier analysis began
as an attempt to approximate periodic functions with in nite summations of
trigonometric polynomials. For certain functions, these sums, known as Fourier
series, converge exactly to the original function. Then next we construct Poisson
kernel by using Fourier series along other trigonometric polynomials, in particular
that they are sum of holomorphic and anti-holomorphic functions.
