The Schwarzchild, respectively the Kerr space-times are solutions for the vacuum Einstein equation which model a spherically symmetric, respectively a rotating black hole. In this talk I will discuss the decay properties of solutions to the linear wave equation on
such backgrounds.

Suppose g is a square integrable function on the real line. The principal shift invariant space, , generated by g is the closure of the span of the system
B ={g(.-k): k an integer}. These spaces are most important in many areas of Analysis. This is particulrly true in the theory of Wavelets. We begin by describing a very simple method for obtaining the basic properties of and the systems B.
The systems obtained by applying, in addition to the integral translations, also the integral modulations (these are the multiplication of a function by exp(-2pinx)) are known as the Gabor systems. By using the Zak transform we show how the same methods can be used to study the basic properties of the Gabor systems and their span.
We will define the Zak transform and explain all this
in a very simple way that will be easily understood by all who know only a "smidgeon" of mathematics. A bit more challenging will be the explanation how all this can be extended to general locally compact abelian groups and their duals.
This is joint work with E. Hernandez, H. Sikic and E. N.
Wilson.

We consider a financial market where the discounted prices of the assets available for trading are modeled by semimartingales that are not assumed to be locally bounded. In this case the appropriate class of admissible integrands is defined through a random variable W that controls the losses incurred in trading. Applying the theory of Orlicz spaces, and convex analysis we study the utility maximization problem with an unbounded random endowment.

We then apply the duality relation to compute the indifference price of a claim satisfying weak integrability conditions. The indifference price leads to a convex risk measure defined on the Orlicz space associated to the utility function.

The talk is based on joint works with S. Biagini and with S. Biagini, M. Grasselli.