Publications

Let Ff be an abolutely convergent Fourier transform on the real line. We extend the following result of K. Karlander to Rn for n≥1: Any closed reflexive subspace {Ff} of the space of continuous functions vanishing at infinity is of finite dimension.

We show that the number of components of the complement of the closure of a coamoeba of an algebraic curve f−1(0) on the complex torus (C∗)2 is at most two times the area of the Newton polygon of f. This is an affirmative answer for the two-dimensional case to a conjecture by Mikael Passare.

We develop a framework for regularly varying measures on complete separable metric spaces S with a closed cone C removed, extending material in [15, 24]. Our framework provides a flexible way to consider hidden regular variation and allows simultaneous regular-variation properties to exist at different scales and provides potential for more accurate estimation of probabilities of risk regions. We apply our framework to iid random variables in ℝ∞<inf>+</inf> with marginal distributions having regularly varying tails and to càdlàg Lévy processes whose Lévy measures have regularly varying tails. In both cases, an infinite number of regular-variation properties coexist distinguished by different scaling functions and state spaces.