球面积分变换是积分几何与凸几何研究中的重要工具.当p为奇数时，给出p-余弦变换是单射的一个直接证明.作为p-余弦变换性质的应用，获得关于凸体唯一性的重要结论：当p为奇数时，星体可由其相应的p-质心体唯一决定.
Spherical integral transformations are indispensable tools in integral geometry and convex geometry. This paper gives a direct proof to the injectivity of p-cosine transformation forp=2k+1, k∈N. Using the injectivity properties of p-cosine transformation, an important result of uniqueness of star body is obtainted, i.e., a star body is uniquely determined by its p-centroid body forp=2k+1, k∈N
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