Lattice points in polytopes, box splines, and Todd operators

Let $X$ be a list of vectors that is totally unimodular. In a previous article the author proved that every real-valued function on the set of interior lattice points of the zonotope defined by $X$ can be extended to a function on the whole zonotope of the form $p(D)B_X$ in a unique way, where $p(D)$ is a differential operator that is contained in the so-called internal \Pcal-space. In this paper we construct an explicit solution to this interpolation problem in terms of Todd operators. As a corollary we obtain a slight generalisation of the Khovanskii-Pukhlikov formula that relates the volume and the number of integer points in a smooth lattice polytope.Comment: 15 pages, 4 figure

Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation

We discuss Laplacians on graphs in a framework of regular Dirichlet forms. We focus on phenomena related to unboundedness of the Laplacians. This includes (failure of) essential selfadjointness, absence of essential spectrum and stochastic incompleteness

Real Asset Returns and Components of Inflation: A Structural VAR Analysis

We shed new light on the negative relationship between real stock returns or real interest rates and (i) ex post inflation, (ii) expected inflation, (iii) unexpected inflation and (iv) changes in expected inflation. Using the structural vector autoregression methodology, we propose a decomposition of those series into economically interpretable components driven by aggregate supply, real demand and money market shocks. Our empirical results support Fama’s ’proxy hypothesis’ and the predictions of several general equilibrium models. Concerning the negative relation between the real rate of interest and inflation, we find that the Mundell-Tobin model and the explanation of Fama and Gibbons (1982) are not competitors: both add insight in their own way about the reasons for the negative correlation between those variables. However, the importance of the latter explanation has decreased since the 1980’s.real stock returns, real rate of interest, expected and unexpected inflation, ’Fisher hypothesis’, structural VAR.