Colloquium - Non-homogeneous tensor products and norms of projections between spaces of polynomials

Speaker: Anthony Brown (University College Dublin)

Abstract: We will introduce the concept of a non-homogeneous symmetric tensor product along with an associated norm, which plays the role of the projective norm on an ordinary tensor product.

With the aid of a duality result, we will use this norm to answer questions about projection mappings between spaces of non-homogeneous polynomials.

We will show that Chebyshev polynomials play a large part in approximately two thirds of the cases. However, the question remains open in the remaining third of cases, and we will show that in these cases, the projection norm does not have to be an integer, indicating that a different type of polynomial is needed.