Gohberg, I.; Kaashoek, M. A. The band extension on the real line as a limit of discrete band extensions. I: The main limit theorem. (English) Zbl 0792.47013 Ando, T. (ed.) et al., Operator theory and complex analysis. Proceedings of a workshop, held in Sapporo, Japan, June 11-14, 1991. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 59, 191-220 (1992). Summary: It is proved that the band extension on the real line (viewed as a convolution operator) may be obtained as a limit in the operator norm of block Laurent operators of which the symbols are band extensions of appropriate discrete approximations of the given data.For the entire collection see [Zbl 0782.00047]. MSC: 47A57 Linear operator methods in interpolation, moment and extension problems 47A20 Dilations, extensions, compressions of linear operators 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) Keywords:band extension on the real line; convolution operator; limit in the operator norm of block Laurent operators PDFBibTeX XMLCite \textit{I. Gohberg} and \textit{M. A. Kaashoek}, in: Operator theory and complex analysis. Proceedings of a workshop, held in Sapporo, Japan, June 11-14, 1991. Basel: Birkhäuser. 191--220 (1992; Zbl 0792.47013)