A Uniqueness Set for the Differential Operator $\Delta_z+\lambda^2$
Mitsuo Morimoto, Ryoko WADA · Tokyo Journal of Mathematics · 1987
We shall show in this paper that this phenomenon occurs locally at the origin.More precisely, we shall prove a semi-local version using the Lie ball.Let $\tilde{B}(\gamma)$ be the Lie ball of radius $r$ with center at the origin in $C^{d+1}$ (see definition in \S 1).The space of holomorphic functions on $\tilde{B}(r)$ is denoted by $\rho(\tilde{B}(\gamma))$ .We shall denote by $P_{\lambda}(\tilde{B}(r))$ the subspace of $d(\tilde{B}(\gamma))$ defined by the differential equation (0.1).Remark that $P_{0}(\tilde{B}(r))=$ $P_{\Delta}(\tilde{B}(r))$ in our notation in our previous paper [8], [10], etc., and that $P_{0}(\tilde{B}(r))$ is the space of harmonic functions on the Lie ball $\tilde{B}(r)$ .Let us consider the space of functions on $M\cap\tilde{B}(\gamma)$ :