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Recent Results and Unsolved Problems on Finite Convolution Operators

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Linear Spaces and Approximation / Lineare Räume und Approximation

Abstract

Finite convolution operators are studied by means of a complex Fourier transform technique. Questions concerning unicellularity and similarity are related to asymptotic properties of bounded analytic functions in a half-plane. The purpose of the paper is to survey recent work, and to call attention to open problems. The theory is illustrated by a list of examples.

Research supported by NSF Grants MCS 76–06297 and MCS 75–04594.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, Lexington, Kentucky, USA

    Richard Frankfurt

  2. Department of Mathematics, University of Virginia, Charlottesville, Virginia, USA

    James Rovnyak

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  1. Richard Frankfurt
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Editor information

Editors and Affiliations

  1. Lehrstuhl A für Mathematik, RWTH Aachen, Templergraben 55, 5100, Aachen, Western Germany

    P. L. Butzer

  2. József Attila Tudományegyetem, Aradi vértanúk tere 1, Szeged, Hungary

    B. Szökefalvi-Nagy

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© 1978 Birkhäuser Verlag Basel

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Frankfurt, R., Rovnyak, J. (1978). Recent Results and Unsolved Problems on Finite Convolution Operators. In: Butzer, P.L., Szökefalvi-Nagy, B. (eds) Linear Spaces and Approximation / Lineare Räume und Approximation. International Series of Numerical Mathematics / Intermationale Schriftenreihe zur Numberischen Mathematik / Sùrie Internationale D’analyse Numùruque, vol 40. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7180-8_13

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  • DOI: https://doi.org/10.1007/978-3-0348-7180-8_13

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-7643-0979-4

  • Online ISBN: 978-3-0348-7180-8

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