Two types of discrete Sobolev inequalities on a weighted Toeplitz graph
Two types of discrete Sobolev inequalities on a weighted Toeplitz graph
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加权托普利茨图上的两种离散索博列夫不等式
DOI：
10.1016/j.laa.2016.06.029
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Yoshinori Kametaka
中科院分区：
文献类型：
--
作者：
Kazuo Takemura;Atsushi Nagai;Yoshinori Kametaka
本文得到了两类对应于加权Toeplitz图上广义图Laplacian A的离散Sobolev不等式。使用绿色矩阵G（a）=（A+ a I）− 1（0< a<∞）和伪格林矩阵G = A <$（A的Penrose-Moore广义逆矩阵）计算尖锐常数C 0（a）和C 0。尖锐常数被表示为对应于每个矩阵A+ aI和A的特征值的调和平均的倒数，除了特征值0。
In this paper, two types of discrete Sobolev inequalities that correspond to the generalized graph Laplacian A on a weighted Toeplitz graph are obtained. The sharp constants C 0 (a) and C 0 are calculated using the Green matrix G (a)=(A+ a I)− 1 (0< a<∞) and pseudo-Green matrix G⁎= A†(Penrose–Moore generalized inverse matrix of A). The sharp constants are expressed as reciprocals of the harmonic mean corresponding to eigenvalues of each matrix A+ a I and A except an eigenvalue 0.