The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

Polyanalytic Functions on Subsets of Z[i]


Abtin Daghighi

Linköping University,
SE-581 83,



For positive integers q we consider the kernel of the powers Lq where L is one of three kinds of discrete analogues of the Cauchy-Riemann operator. The first two kinds are well-studied, 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 pseudo-powers. We propose such multiplications together with associated pseudo-powers. We develop a proof-tool in terms of certain sets of uniqueness.

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