Endomorphisms of Banach algebras of infinitely differentiable functions on compact plane sets

In this note we study the endomorphisms of certain Banach algebras of infinitely differentiable functions on compact plane sets, associated with weight sequences M. These algebras were originally studied by Dales, Davie and McClure. In a previous paper this problem was solved in the case of the unit interval for many weights M. Here we investigate the extent to which the methods used previously apply to general compact plane sets, and introduce some new methods. In particular, we obtain many results for the case of the closed unit disc. This research was supported by EPSRC grant GR/M31132Comment: 15 pages LaTe

Subcritical Lp bounds on spectral clusters for Lipschitz metrics

We establish asymptotic bounds on the L^p norms of spectrally localized functions in the case of two-dimensional Dirichlet forms with coefficients of Lipschitz regularity. These bounds are new for the range p>6. A key step in the proof is bounding the rate at which energy spreads for solutions to hyperbolic equations with Lipschitz coefficients.Comment: 10 page

Subcritical Lp bounds on spectral clusters for Lipschitz metrics

We establish asymptotic bounds on the L^p norms of spectrally localized functions in the case of two-dimensional Dirichlet forms with coefficients of Lipschitz regularity. These bounds are new for the range p>6. A key step in the proof is bounding the rate at which energy spreads for solutions to hyperbolic equations with Lipschitz coefficients.Comment: 10 page

The Lewis Strain Gauge Laboratory: Status and plans

An in-house lab was established for developing, testing, and evaluating high-temperature strain gauges and to aid in in-house applications of high-temperature strain instrumentation. The lab is automated to provide computer control of oven temperatures, imposed strain, and data sampling