In this paper we g i v e some necessary and su cient conditions for uniform approximability of functions by polyanalytic polynomials on plane compact sets of special form. Also connections with the corresponding Dirichlet problem are considered.

Three variants of the Schiff equation are investigated to model the spectra produced by megavoltage linear accelerators. These models are tested against well-validated Monte Carlo (MC) generated spectra on the central axis of large-area fields, and show excellent agreement. Numerical reconstructions of 6 and 10 MV spectra using the same models are then presented, using experimental attenuation data derived from an electronic portal imager. The process of deriving spectra from experimental attenuation data is shown to be inherently badly constrained mathematically, with the derived spectrum being highly sensitive to noise in the source data, and non-unique. By placing a priori constraints on the Schiff model from both physical knowledge of the construction of the accelerator and MC data, physically useful results are gained and presented for both the energy dependence and off-axis behaviour of photon spectra.

No abstract

ABSTRACT. We study approximations of functions by n-analytic polynomials in the uniform norm on closed rectifiable Jordan curves in the complex plane. It is shown that, in contrast to the case of uniform approximations by complex polynomials, there are no topological criteria for the existence of such approximations. We obtain a criterion for the existence of n-tmalytic polynomial approximations in terms of analytic properties of these curves.

No abstract