Discrete function theory based on skew Weyl relations

De Ridder, Hilde; De Schepper, Hennie; Kähler, Uwe; Sommen, Frank

doi:10.1090/S0002-9939-2010-10480-X

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.

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