永久向量

摘要：

恒常向量是具有高斯向量的分量的平方的分量的向量的推广，在这个意义上，出现在高斯平方向量的拉普拉斯变换中的矩阵不需要是对称的或正定的。此外，高斯平方向量的拉普拉斯变换中行列式的幂为-1/2，允许为小于小于零的任何数。我们根本不清楚什么向量是恒向量。本文刻画了$R^{3}_{+}$中的所有永久向量，并给出了$R^{n}_{+}$中永久向量和永久过程研究中的应用.

英文摘要：

A permanental vector is a generalization of a vector with components that are squares of the components of a Gaussian vector, in the sense that the matrix that appears in the Laplace transform of the vector of Gaussian squares is not required to be either symmetric or positive definite. In addition the power of the determinant in the Laplace transform of the vector of Gaussian squares, which is -1/2, is allowed to be any number less than zero. It was not at all clear what vectors are permanental vectors. In this paper we characterize all permanental vectors in $R^{3}_{+}$ and give applications to permanental vectors in $R^{n}_{+}$ and to the study of permanental processes.

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