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A generalized Leibniz rule and foundation of a discrete quaternionic analysis. (English) Zbl 0659.30041

Geometry and physics, Proc. Winter Sch., Srnî/Czech. 1987, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 16, 43-64 (1987).
[For the entire collection see Zbl 0634.00015.]
This paper presents some new results in the real quaternionic analysis. First of all the authors give a generalized Leibniz rule for quaternionic-valued functions. Further, they present a model of a discrete function theory of quaternions. Finally, they deduce formulas of representation of solutions of the discrete Laplace equation and describe the orthogonal complement of the space of discrete-analytic functions in \(L_ 2\).
Reviewer: A.D.Mednych

MSC:

30G30 Other generalizations of analytic functions (including abstract-valued functions)
30G25 Discrete analytic functions

Citations:

Zbl 0634.00015