中文摘要：

自仿测度μ_M,D的谱与非谱问题是自仿测度谱理论研究的主要内容之一,而μ_M,D-正交指数系的有限性或无限性问题在研究自仿测度是否为谱测度中起着重要的作用.本文主要探讨空间自仿测度下无限正交指数系存在的条件.通过利用函数m_D（x）零点集Z（m_D）中的非零中间点（即坐标为0或1/2的点）的性质,得到存在无限μ_（M,D）-正交指数系的许多条件,为进一步研究自仿测度μ_（M,D）的谱性质奠定基础.

英文摘要：

The question of determining the spectrality or non-spectrality of a self-affine measures μ_（m,d） is one of the important subject in the spectral theory of self-affine measures.In this regard,the finiteness or infiniteness of μ_（M,D）-orthogonal exponentials plays a central role.We study in this paper the conditions of infinite orthogonal exponentials under the spatial selfaffine measures.By using the middle points of the zero set Z（m_D） of the function m_D（x）,we obtain some conditions under which μ_（M,D）-orthogonal exponentials is infinite.Such research is necessary for further understanding the spectrality of self-affine measures.