On the eigenvalues of certain Hermitian operators
On the eigenvalues of certain Hermitian operators
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关于某些 Hermitian 算子的特征值
DOI：
10.1090/s0002-9947-1958-0098321-8
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发表时间：
1958
影响因子：
1.3
通讯作者：
H. Widom
中科院分区：
文献类型：
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作者：
H. Widom
对于一般核p(x)，证明的很少，但怀疑的却很多。Bellman和Latter[1]已经为相当一般的p得到了（1.1）的最大特征值的上界和下界，然而，对于大多数有趣的核来说，这些边界相当弱。更重要的是卡茨、默多克和塞戈的猜想。设p(x) > 0 end f0(1 +x2)p(x)dx< c。用表示（1.1）的正特征值
As for general kernels p(x), little has been proved but much has been suspected. Bellman and Latter [1] have obtained upper and lower bounds for the largest eigenvalue of (1.1) for quite general p, these bounds, however, being rather weak for most interesting kernels. More to the point is a conjecture of Kac, Murdock, and Szego [5]. Assume p(x) > 0 end f0(1 +x2)p(x)dx< c. Denote the positive eigenvalues of (1.1) by