Paley--Wiener Theorems for the U(n)--spherical transform on the Heisenberg group

We prove several Paley--Wiener-type theorems related to the spherical transform on the Gelfand pair $\big(H_n\rtimes U(n),U(n)\big)$, where $H_n$ is the $2n+1$-dimensional Heisenberg group. Adopting the standard realization of the Gelfand spectrum as the Heisenberg fan in ${\mathbb R}^2$, we prove that spherical transforms of $U(n)$--invariant functions and distributions with compact support in $H_n$ admit unique entire extensions to ${\mathbb C}^2$, and we find real-variable characterizations of such transforms. Next, we characterize the inverse spherical transforms of compactly supported functions and distributions on the fan, giving analogous characterizations

The synthesis, characterization and thermal chemistry of modified norbornenyl PMR endcaps

As part of a program to further the understanding of the polymerization of Nadic-Endcapped PMR systems, a series of model Norbornenyl-Imides has been synthesized and their thermal behavior explored. Their syntheses and characterizations as well as their rearrangement and polymerization chemistry are described. Monomer isomerization at temperatures as low as 125 C and oligomer formation at somewhat higher temperatures are observed. Approximate relative rates for competing isomerization pathways are established and some information is obtained about the details of oligomer formation. The relationship of this data to current PMR systems is briefly discussed