


Paper Title:
Polyanalytic Functions on Subsets of Z[i]
Author(s):
Abtin Daghighi
Linköping University,
SE581 83,
Sweden.
Email: abtindaghighi@gmail.com
Abstract:
For positive integers q we consider the kernel of the powers L^{q} where L is one of three kinds of discrete analogues of the CauchyRiemann operator. The first two kinds are wellstudied, but the third kind less so. We give motivations for further study of the third kind especially since its symmetry makes it more appealing for the cases q≥ 2.
From an algebraic perspective it makes sense that the chosen multiplication on the kernels is compatible with the choice of pseudopowers. We propose such multiplications together with associated pseudopowers. We develop a prooftool in terms of certain sets of uniqueness.
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