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Discrete function theory based on skew Weyl relations


Authors: Hilde De Ridder, Hennie De Schepper, Uwe Kähler and Frank Sommen
Journal: Proc. Amer. Math. Soc. 138 (2010), 3241-3256
MSC (2010): Primary 39A12, 30G35, 39A70, 06D50
DOI: https://doi.org/10.1090/S0002-9939-2010-10480-X
Published electronically: May 13, 2010
MathSciNet review: 2653954
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Abstract: In this paper we construct the main ingredients of a discrete function theory in higher dimensions by means of a new ``skew'' type of Weyl relations. We will show that this new type overcomes the difficulties of working with standard Weyl relations in the discrete case. A Fischer decomposition, Euler operator, monogenic projection, and basic homogeneous powers will be constructed.


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Additional Information

Hilde De Ridder
Affiliation: Clifford Research Group, Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Galglaan 2, 9000 Gent, Belgium
Email: hdr@cage.UGent.be

Hennie De Schepper
Affiliation: Clifford Research Group, Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Galglaan 2, 9000 Gent, Belgium
Email: hds@cage.UGent.be

Uwe Kähler
Affiliation: Departamento de Matemática, Universidade de Aveiro, Aveiro, 3810-193 Centro, Portugal
Email: ukaehler@ua.pt

Frank Sommen
Affiliation: Clifford Research Group, Department of Mathematical Analysis, Faculty of Sciences, Ghent University, Galglaan 2, 9000 Gent, Belgium
Email: fs@cage.ugent.be

DOI: https://doi.org/10.1090/S0002-9939-2010-10480-X
Keywords: Discrete monogenic polynomial, Fischer decomposition
Received by editor(s): December 17, 2009
Published electronically: May 13, 2010
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2010 American Mathematical Society