This project is mathematical research in function theory and operator theory. Three lines of investigation will be pursued. The first involves polynomial approximation relative to certain kinds of measures supported in the closed unit disc. The second area involves problems concerning composition operators on various spaces of analytic functions in the disc and in the unit ball in complex n-space; this includes questions of boundedness and norm estimates, compactness, and spectral properties of composition operators. Finally, a study of commuting holomorphic self-maps of the n-ball will be initiated.
