We study the spectral theory and inverse problem on asymptotically hyperbolic manifolds.
The main subjects are as follows:(1) Location of the essential spectrum.(2) Absence of …

We prove a Paley-Wiener theorem for a class of symmetric spaces of the compact type, in
which all root multiplicities are even. This theorem characterizes functions of small support in …

Let $\a $ be an Euclidean vector space of dimension $ N, $ and let $ k=(k_\alpha) _
{\alpha\in\cal R} $ be a multiplicity function related to a root system $\cal R. $ Let $\Delta (k) …

The fundamental solution K (y| x, t) of the heat equation (1. 1) ut= uxx+ V (x) u, u (x, 0)= δ (x−
y), has been linked with soliton theory from the early days [30], by providing a tool for …

We consider the heat equation ut= Lu where L is a second-order difference operator in a
discrete variable n. The fundamental solution has an expansion in terms of the Bessel …

The following standard notation will be used. In a metric space X with metric d, C (X) denotes
the space of continuous complex-valued functions, Br (x) denotes the open ball {y EX: d (x …

In this paper we analyze the heat kernel of the equation∂ tv=±L v, where L=∂ x N+ u N− 2
(x)∂ x N− 2+⋯+ u 0 (x) is an N-th order differential operator and the±sign on the right-hand …

In this paper we construct the fundamental solution to the Schödinger equation on a
compact symmetric space with even root multiplicities using shift operators of Heckman and …

The physical notion of Huygens' Principle goes back to the classical “Traité de la Lumière”
by Christian Huygens, published in 1690. Various aspects of this fundamental principle in …

These notes began as lectures that I intended to deliver in Edinburgh in April, 1999.
Unfortunately I was not able to leave Australia at the time. Since then there has been …