%0 Journal Article
%A Cobos Díaz, Fernando
%A Fernández-Martínez, Pedro
%T Dependence on Parameters in Interpolation Methods Associated to Polygons
%D 1995
%@ 0041-7084
%U https://hdl.handle.net/20.500.14352/57315
%X A theorem due to S. Janson, P. Nilsson, J. Peetre and M. Zafran [Proc. Lond. Math. Soc., III. Ser. 48, 283-299 (1984; Zbl 0532.46046)] states that for a Banach couple A such that _(A) is not closed in _(A) the real interpolation spaces A_,q and A_,p coincide if and only if _ = _ and p = q. Here the analogous problem for N-tuples of Banach spaces is investigated. It is assumed that the N-tuple A satisfies a certain condition "(A) which ensures that the J- and the K-methods with respect to a polygon _ coincide. Also, it is assumed that _(A) is not closed in _(A).The authors prove the following results:(1) If P,Q 2 int _ and AP,p = AQ,q, then p = q.(2) If P, Q,R 2 int _ and AP,q = AQ,q = AR,q, then P, Q and R are affinely dependent.
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