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Dependence on Parameters in Interpolation Methods Associated to Polygons

Cobos, Fernando and Fernández-Martínez, Pedro (1995) Dependence on Parameters in Interpolation Methods Associated to Polygons. Bollettino della Unione Matematica Italiana, 9B (2). pp. 339-357. ISSN 0041-7084

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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Real interpolation method defined by a polygon; real interpolation spaces
Subjects:Sciences > Mathematics > Numerical analysis
ID Code:15476
Deposited On:05 Jun 2012 09:22
Last Modified:21 Oct 2013 17:20

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