Let {zn} denote a fixed
sequence of complex numbers in the unit disc satisfying (1 −|zn+1|2)∕(1 −|zn|2) ≦ δ < 1
for some δ. Let M be a nonnegative integer, and let m be generic for integers
between 0 and M inclusive. We define the linear functionals Ln[m] on H2 by
Ln[m]f = f(m)(zn). Given M + 1 sequences w[0],⋯,w[M] in l2, can there be found
a function f in H2 which solves the simultaneous weighted interpolation
problem
Shapiro and Shields considered this problem for M = 0. Their results were
generalized by the author to the case M = 1. The purpose of this paper is to extend
this generalization to arbitrary M.
![f (m )(zn) = (w[m])n∥L [mn]∥?](a200x.png)
