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Discrete function theory based on skew Weyl relations
Author(s):
Hilde
De Ridder;
Hennie
De Schepper;
Uwe
Kähler;
Frank
Sommen
Journal:
Proc. Amer. Math. Soc.
138
(2010),
3241-3256.
MSC (2010):
Primary 39A12, 30G35, 39A70, 06D50
Posted:
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:
10.1090/S0002-9939-2010-10480-X
PII:
S 0002-9939(2010)10480-X
Keywords:
Discrete monogenic polynomial,
Fischer decomposition
Received by editor(s):
December 17, 2009
Posted:
May 13, 2010
Communicated by:
Michael T. Lacey
Copyright of article:
Copyright
2010,
American Mathematical Society
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