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Papers by Henry Cheng
New Zealand Journal of Mathematics
We establish analogues of Liouville's theorem in the complex function theory, with the differ... more We establish analogues of Liouville's theorem in the complex function theory, with the differential operator replaced by various difference operators. This is done generally by the extraction of (formal) Taylor coefficients using a residue map which measures the obstruction having local "anti-derivative". The residue map is based on a Weyl algebra or qqq-Weyl algebra structure satisfied by each corresponding operator. This explains the different senses of "boundedness" required by the respective analogues of Liouville's theorem in this article.
New Zealand Journal of Mathematics
We establish analogues of Liouville's theorem in the complex function theory, with the differ... more We establish analogues of Liouville's theorem in the complex function theory, with the differential operator replaced by various difference operators. This is done generally by the extraction of (formal) Taylor coefficients using a residue map which measures the obstruction having local "anti-derivative". The residue map is based on a Weyl algebra or qqq-Weyl algebra structure satisfied by each corresponding operator. This explains the different senses of "boundedness" required by the respective analogues of Liouville's theorem in this article.