Discrete function theory based on skew Weyl relations

• DOI: 10.1090/s0002-9939-2010-10480-x
• Publication Date: 2010-10-13T20:21:01Z
• Authors: Hilde De Ridder; Hennie De Schepper; Uwe Kähler; Frank Sommen
• Keywords: 0101 mathematics; 01 natural sciences

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.