We study the problem whether a given $2$-dimensional symmetric stable distribution with index $\alpha$ $(0 < \alpha \leq 1)$ is determined by its $1$-dimensional projections in some specified directions. We give some conditions for the affirmative answer and for the negative answer.
"Two-dimensional symmetric stable distributions and their projections." Nagoya Math. J. 180 135 - 149, 2005.