TY - JOUR
T1 - A Discrete Bochner-Martinelli Formula
AU - Bory-Reyes, Juan
AU - Sommen, Frank
N1 - Funding Information:
Acknowledgments This paper was written while the first author was visiting the Department of Mathematical Analysis of Ghent University. He was supported by Research Foundation on Flanders (F.W.O.-project 31506208). Juan Bory Reyes wishes to thank the members of Clifford Research Group in Ghent for their kind hospitality.
PY - 2011/3
Y1 - 2011/3
N2 - In the even dimensional case the discrete Dirac equation may be reduced to the so-called discrete isotonic Dirac system in which suitable Dirac operators appear from both sides in half the dimension. This is an appropriated framework for the development of a discrete Martinelli-Bochner formula for discrete holomorphic functions on the simplest of all graphs, the rectangular ℤ one. Two lower-dimensional cases are considered explicitly to illustrate the closed analogy with the theory of continuous variables and the developed discrete scheme.
AB - In the even dimensional case the discrete Dirac equation may be reduced to the so-called discrete isotonic Dirac system in which suitable Dirac operators appear from both sides in half the dimension. This is an appropriated framework for the development of a discrete Martinelli-Bochner formula for discrete holomorphic functions on the simplest of all graphs, the rectangular ℤ one. Two lower-dimensional cases are considered explicitly to illustrate the closed analogy with the theory of continuous variables and the developed discrete scheme.
KW - Bochner-Martinelli transform
KW - Discrete Clifford analysis
UR - http://www.scopus.com/inward/record.url?scp=79951942452&partnerID=8YFLogxK
U2 - 10.1007/s11785-009-0038-9
DO - 10.1007/s11785-009-0038-9
M3 - Artículo
SN - 1661-8254
VL - 5
SP - 83
EP - 95
JO - Complex Analysis and Operator Theory
JF - Complex Analysis and Operator Theory
IS - 1
ER -