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Saturation theorems for interpolation and the Bernstein-Schnabl operator


Authors: Marek Beska and Karol Dziedziul
Journal: Math. Comp. 70 (2001), 705-717
MSC (2000): Primary 41A15, 41A35, 41A25, 41A65, 41A40, 41A05
DOI: https://doi.org/10.1090/S0025-5718-00-01173-X
Published electronically: November 27, 2000
MathSciNet review: 1677470
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Abstract | References | Similar Articles | Additional Information

Abstract:

We shall study properties of box spline operators: cardinal interpolation, convolution, and the Bernstein-Schnabl operator. We prove the saturation theorem.


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Additional Information

Marek Beska
Affiliation: Technical University of Gdańsk, Faculty of Applied Mathematics, ul. Narutowicz 12/12, 80-952 Gdańsk, Poland
Email: beska@mifgate.pg.gda.pl

Karol Dziedziul
Affiliation: Technical University of Gdańsk, Faculty of Applied Mathematics, ul. Narutowicz 12/12, 80-952 Gdańsk, Poland
Email: kdz@mifgate.pg.gda.pl

DOI: https://doi.org/10.1090/S0025-5718-00-01173-X
Keywords: Box splines, cardinal interpolation, convolution operators, the Bernstein-Schnabl operator, Randon-Nikodym property, the saturation theorem.
Received by editor(s): March 17, 1998
Received by editor(s) in revised form: October 23, 1998, and February 4, 1999
Published electronically: November 27, 2000
Article copyright: © Copyright 2000 American Mathematical Society

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