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Function cones and interpolation

✍ Scribed by Joan Cerdà; Heribert Coll

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
207 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

We consider interpolation of operators acting on functions that belong to a given cone Q with the so-called decomposition property. The set of all positive functions whose level sets are the level sets of a given function is the main example, and the cone of all decreasing functions is a particular case. As applications, we obtain conditions for the identity (E0 ∩ Q, E1 ∩ Q) θ,p = (E0, E1) θ,p ∩ Q and interpolation results for operators which are bounded when restricted to a given family of characteristic funcions.

📜 SIMILAR VOLUMES

Interpolation Formulas and Auxiliary Fun
Interpolation Formulas and Auxiliary Functions
✍ Damien Roy 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 279 KB

We prove an interpolation formula for ``semi-cartesian products'' and use it to study several constructions of auxiliary functions. We get in this way a criterion for the values of the exponential map of an elliptic curve E defined over Q. It reduces the analogue of Schanuel's conjecture for the ell