Simultaneous saturation in connection with dirichlet's problem for a wedge

Abstract

This paper is concerned with an extension of the classical concept of staturation to systems of coupled approximations. Let {T j , ϑ}, j=1,2 be two families of bounded linear operators of the product space Y×Y into (the Banach space) y which constitute a strong simultaneous approximation process on Y×Y in the sense that for each and j=1,2 where . The simultaneous process {T j , ϑ} is then said to be saturated on Y×Y if there exist φ j (ϑ) with such that every for which is an invariant elements under {T j , ϑ} and if the set , the so-called Favard class, contains at least one noninvariant element. On the basis of this concept the boundary behavior of the solution of Dirichlet's problem for a wedge is studied in detail as an application of general results on simultaneous approximation processes of Mellin convolution;matrix-methods are employed.