Weighted norm inequalities for convolution operators and links with the Weiss Conjecture

We study convolution operators on weighted Lebesgue spaces and obtain weight characterisations for boundedness of these operators with certain kernels. Our main result is Theorem 3 which enables us to obtain results for certain kernel functions supported on bounded intervals; in particular we get a direct proof of the known characterisations for Steklov operators in Section 3 by using the weighted Hardy inequality. Our methods also enable us to obtain new results for other kernel functions in Section 4. In Section 5 we demonstrate that these convolution operators are related to operators arising from the Weiss Conjecture (for scalar-valued observation functionals) in linear systems theory, so that results on convolution operators provide elementary examples of nearly bounded semigroups not satisfying the Weiss Conjecture. Also we apply results on the Weiss Conjecture for contraction semigroups to obtain boundedness results for certain convolution operators.     

Decay of a polariton mode generated by difference mixing

An experiment to determine the life-time of a pulsed polariton is analysed. (i) The phase matching condition for a complex refractive index is discussed, and (ii) decay curves are presented for both polariton branches.     

Technological forecasting in planning for company growth

No one company has resources that are sufficient to permit it to counter all potential threats or to explore all available opportunities resulting from today's technology explosion. Accordingly, each company must become increasingly selective in its allocation of those resources committed toward insuring its future. This article describes the particular experience of TRW Inc. with technological forecasting?one of several techniques that a company may use in improving its selectivity.     

A high-power pulsed xenon ion laser

Over 80 kW of peak power has been obtained on the combined visible lines of a pulsed xenon ion laser. Light pulse shapes of the strongest lines are discussed.