Speaker
Description
In this talk we will consider the following central problem on the uniform approximation by homogeneous polynomials:
For which 0-symmetric star like domains $K\subset \mathbb R^d$ and which $f\in C(\partial K)$ there exist homogeneous polynomials $h_{n}, h_{n+1}$ of degree $n$ and $n+1$, respectively, so that uniformly on $\partial K$
$$f=\lim_{n\rightarrow \infty}(h_{n}+h_{n+1})? $$
This is the analogue of the classical Weierstrass approximation problem with polynomials of total degree being replaced by homogeneous polynomials.
The answer to the above problem has an intrinsic connection to the geometry of the underlying domain. We will give a survey of various results related to the above question and will also list some important open problems.
