TY - JOUR
AU - Cheng, Kam Hang
AU - Chiang, Yik Man
AU - Ching, Avery
PY - 2022/10/25
Y2 - 2022/12/08
TI - D-module approach to Liouville's Theorem for difference operators
JF - New Zealand Journal of Mathematics
JA - NZ J Math
VL - 53
IS -
SE - Articles
DO - 10.53733/187
UR - https://nzjmath.org/index.php/NZJMATH/article/view/187
SP - 63--79
AB - <p>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 $q$-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.</p>
ER -