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Zeitschrift für Analysis und ihre Anwendungen


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Volume 12, Issue 1, 1993, pp. 27–67
DOI: 10.4171/ZAA/581

Published online: 1993-03-31

Weithed Spaces of Pseudocontinuable Functions and Approximations by Rational Functions with Prescribed Poles

Victor Katsnelson[1]

(1) Weizmann Institute of Science, Rehovot, Israel

The main result of this paper provides an essential intermediate step for the proof of the authors theorem on left and right Blaschke-Potapov products which yields more insight into the structure of $J$-inner functions. The goal of this paper is to prepare an appropriate backward Schur-Potapov algorithm by solving a weighted approximation problem.

Keywords: Spectral synthesis, Blaschke-Potapov products, $J$-contractive analytic matrix-valued functions, Arov-singular $J$-inner matrix-valued functions, rational approximation

Katsnelson Victor: Weithed Spaces of Pseudocontinuable Functions and Approximations by Rational Functions with Prescribed Poles. Z. Anal. Anwend. 12 (1993), 27-67. doi: 10.4171/ZAA/581