On a conjecture of C. A. Micchelli concerning cubic spline interpolation at a biinfinite knot sequence

AbstractIt is shown that if the knot sequence t:= (ti)−∞∞ satisfies (i) for some m ϵ ¦ 1, (3 + √5)2), m−1⩽limrinfiti+r−1 − ti+rti+1 − ti ⩽ limrsupiti+r+1 − ti+rti+1 − ti ⩽ m and (ii) mt:= sup|i−j|⩽1ti+1 − titj+1 − tj ≤ ∞ then for any given bounded sequence y ε m(Z) there exists exactly one bounded cubic spline s with knots ti such that s(ti) = yi for all i ε Z