固定阶矩阵单调性和凸性的局部刻画
Local characterizations for the matrix monotonicity and convexity of fixed order
摘要：
我们建立了局部特征的矩阵单调性和凸性的固定顺序，通过给整表示连接Loewner和Kraus矩阵，以前已知的这些属性的特征，各自的汉克尔矩阵。我们的结果是新的已经在一般情况下的矩阵凸性和我们的方法显着简化了相应的工作矩阵单调性。我们还得到了Kraus关于矩阵凸性的一个推广，并加强了单调性和凸性之间的关系。
英文摘要：
We establish local characterizations of matrix monotonicity and convexity of fixed order by giving integral representations connecting the Loewner and Kraus matrices, previously known to characterize these properties, to respective Hankel matrices. Our results are new already in the general case of matrix convexity and our approach significantly simplifies the corresponding work on matrix monotonicity. We also obtain an extension of the original characterization for matrix convexity by Kraus, and tighten the relationship between monotonicity and convexity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
