Double piling structure of matrix monotone functions and of matrix convex functions II
Double piling structure of matrix monotone functions and of matrix convex functions II
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矩阵单调函数与矩阵凸函数的双堆积结构II
DOI：
10.1016/j.laa.2012.02.033
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发表时间：
2012
影响因子：
1.1
通讯作者：
J. Tomiyama
中科院分区：
文献类型：
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作者：
H. Osaka;J. Tomiyama
我们继续分析[H. Osaka, J. Tomiyama，矩阵单调函数和矩阵凸函数的双重堆积结构，线性及其应用 431 (2009) 1825–1832] 其中讨论了每个标签 n 的以下三个断言：我们知道两个条件 (2) 和 (3) 是等价的，并且如果 f 且 f(0)≤0 是 n-凸的，则 g 是 (n-1)-单调的。在本文中，我们考虑 f 或 g 的几个额外条件来得出结论，从 (3) 到 (1) 的含义是正确的。特别地，我们研究了具有条件正 Lowner 矩阵的函数类 Qn([0,α))，其中包含矩阵 n-单调函数类，并表明如果 f∈Qn+1([0,α)) 且 f(0)=0 并且 g 是 n-单调，则 f 是 n-凸。我们还讨论了 n 凸性的局部性质。
We continue the analysis in [H. Osaka, J. Tomiyama, Double piling structure of matrix monotone functions and of matrix convex functions, Linear and its Applications 431 (2009) 1825–1832] in which the followings three assertions at each label n are discussed: We know that two conditions (2) and (3) are equivalent and if f with f(0)≤0 is n-convex, then g is (n-1)-monotone. In this note we consider several extra conditions on f or g to conclude that the implication from (3) to (1) is true. In particular, we study a class Qn([0,α)) of functions with conditional positive Lowner matrix which contains the class of matrix n-monotone functions and show that if f∈Qn+1([0,α)) with f(0)=0 and g is n-monotone, then f is n-convex. We also discuss about the local property of n-convexity.