Vol. 27, No. 3, 1968

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ISSN: 0030-8730
Simultaneous interpolation in H2. II

Jordan Tobias Rosenbaum

Vol. 27 (1968), No. 3, 607–610
Abstract

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

f (m )(zn) = (w[m])n∥L [mn]∥?

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.

Mathematical Subject Classification
Primary: 30.67
Milestones
Received: 24 July 1967
Published: 1 December 1968
Authors
Jordan Tobias Rosenbaum