On the complex moment problem on radial rays

Анотація

The complex moment problem in the case when the support of the measure lies on the algebraic curves $P_N=\left\{z\in \mathbb{C}: z^N -\overline{z}^N=0\right\}$, $N=1,2,3,\ldots$, is studied. For $N=2,3$ the necessary and sufficient conditions of solvability are obtained and all solutions of the problem are described. It is shown how this problem for arbitrary $N$ is connected with the Hamburger moment problem with parameters.

Mathematics Subject Classification: 44A60.