Discrete function theory based on skew Weyl relations
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- by Hilde De Ridder, Hennie De Schepper, Uwe Kähler and Frank Sommen PDF
- Proc. Amer. Math. Soc. 138 (2010), 3241-3256 Request permission
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.References
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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
- Received by editor(s): December 17, 2009
- Published electronically: May 13, 2010
- Communicated by: Michael T. Lacey
- © Copyright 2010 American Mathematical Society
- 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
- MathSciNet review: 2653954