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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.
The contribution of this author was supported by a DFG research grant
The contribution of this author was supported by a DFG research grant
Notes
The contribution of this author was supported by a DFG research grant