On extremal properties of Jacobian elliptic functions with complex modulus
On extremal properties of Jacobian elliptic functions with complex modulus
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复模雅可比椭圆函数的极值性质
DOI：
10.1016/j.jmaa.2016.05.008
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发表时间：
2015
影响因子：
1.3
通讯作者：
Frantivsek vStampach
中科院分区：
文献类型：
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作者：
P. Siegl;Frantivsek vStampach
对函数m ∈ Sn（K（m）u）值的深入分析|m），且u∈（0，1）.首先，证明了如果m不属于C中由不等式确定的区域，则该函数的绝对值永远不超过1| z− 1| < 1且|z|> 1.所研究的函数的全局最大值总是位于该区域。更精确地说，证明了如果u≤ 1/2，则全局最大值位于m= 1且值等于1。而如果u> 1/2，则全局最大值位于区间（1，2）中，并且其值超过1。此外，更微妙的极值性质进行了数值研究。最后给出了复Jacobi矩阵的Laplace型积分和谱分析中的应用。
A thorough analysis of values of the function m↦ sn (K (m) u| m) for complex parameter m and u∈(0, 1) is given. First, it is proved that the absolute value of this function never exceeds 1 if m does not belong to the region in C determined by inequalities| z− 1|< 1 and| z|> 1. The global maximum of the function under investigation is shown to be always located in this region. More precisely, it is proved that if u≤ 1/2, then the global maximum is located at m= 1 with the value equal to 1. While if u> 1/2, then the global maximum is located in the interval (1, 2) and its value exceeds 1. In addition, more subtle extremal properties are studied numerically. Finally, applications in a Laplace-type integral and spectral analysis of some complex Jacobi matrices are presented.
雅可比函数的差分公式
DOI：
--
发表时间：
2007
期刊：
影响因子：
--
作者：
Takeshi;Kawazoe;Takeshi Kawazoe;Takeshi Kawazoe
通讯作者：
Takeshi Kawazoe