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An introduction to complex functions on products of two time scales. (English) Zbl 1105.30034

The authors introduce analytic functions of a complex time scale variable \(T_1+iT_2\). In particular, if \(T_1=T_2\) is the set of real numbers, we arrive at the classic analytic functions. If \(T_1=T_2\) is the set of integers, we obtain discrete analytic functions. The delta partial derivative is defined in such a way that in the discrete case it becomes a difference operator. Using the delta derivative the authors develop the “delta complex analysis”: the Cauchy-Riemann equations, integrals along time scale curves, the Cauchy integral theorem.

MSC:

30G25 Discrete analytic functions
39A10 Additive difference equations
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References:

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