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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)
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