环面不变复Minkowski空间中分布的余弦变换的值域
On the Range of Cosine Transform of Distributions for Torus-Invariant Complex Minkowski Spaces
摘要：
本文研究了（绝对值）余弦变换的值域，利用积分方程中的Fredholm定理证明了一个推广的满射性定理，并给出了\mathbb{C}^n上复Minkowski度量的Hermitian特征定理.利用初等线性代数方法对Grassmannian进行了参数化，并通过计算分布的Legendre级数展开式中的系数，给出了Grassmannian Gr_{2}（\mathbb{C}^{2}）上分布空间的（绝对值）余弦变换的象的特征.
英文摘要：
In this paper, we study the range of (absolute value) cosine transforms for which we give a proof for an extended surjectivity theorem by making applications of the Fredholm's theorem in integral equations, and show a Hermitian characterization theorem for complex Minkowski metrics on \mathbb{C}^n. Moreover, we parametrize the Grassmannian in an elementary linear algebra approach, and give a characterization on the image of the (absolute value) cosine transform on the space of distributions on the Grassmannian Gr_{2}(\mathbb{C}^{2}), by computing the coefficients in the Legendre series expansion of distributions.
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