An outer function and several important functions in two variables

摘要

In this paper we study the properties of an outer function in function theory, operator theory, functional analysis and prediction theory. Outer functions have been studied by W. Rudin [13], K. Izuchi [7], K. Izuchi-Y. Matsugu [8] and R. Cheng [2]. In two variables, an outer function is too strong in some sense. If h is a nonzero function in H", then the following inequalities are valid. mz and mw denote the normalized Lebesgue measures on the unit circle T=T_z and T=T_w. T~2=TxT and m=m_zXm_2.