@article{Cichoń_Stochel_Szafraniec_2019, title={The complex moment problem: determinacy and extendibility}, volume={124}, url={https://www.mscand.dk/article/view/112091}, DOI={10.7146/math.scand.a-112091}, abstractNote={<p>Complex moment sequences are exactly those which admit positive definite extensions on the integer lattice points of the upper diagonal half-plane. Here we prove that the aforesaid extension is unique provided the complex moment sequence is determinate and its only representing measure has no atom at $0$. The question of converting the relation is posed as an open problem. A partial solution to this problem is established when at least one of representing measures is supported in a plane algebraic curve whose intersection with every straight line passing through $0$ is at most one point set. Further study concerns representing measures whose supports are Zariski dense in $\mathbb{C} $ as well as complex moment sequences which are constant on a family of parallel “Diophantine lines”. All this is supported by a bunch of illustrative examples.</p>}, number={2}, journal={MATHEMATICA SCANDINAVICA}, author={Cichoń, Dariusz and Stochel, Jan and Szafraniec, Franciszek Hugon}, year={2019}, month={Jun.}, pages={263–288} }