在双无限节点序列上插值的简单双曲样条的C.A.Micchelli猜想

On a Conjecture of C. A. Micchelli Concering Simple Hyperbolic Splime Interpolation at a Biinflnite Sequence

本文指出当节点序列t=(t_i)_(-∞)~∞满足一定的条件时,则对任意给定的有界序列ye(Z)这里恰好存在一个具有节点t_i的有界双曲样条H对所有i∈Z使得H(t_i)=y_i。

It is shown that if the knot sequence t= (ti) x. satisfies (i) for some m∈[1, (3+ ) /2] and (ii) theu for any given bounded sequence y∈m (Z) there exactly one bounded simple hyperbolic spline H with knots ti such H (ti) =yi for all i∈Z.