The norms and singular numbers of polynomials of the classical Volterra operator in L2(0,1)
The norms and singular numbers of polynomials of the classical Volterra operator in L2(0,1)
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L2(0,1) 中经典 Volterra 算子多项式的范数和奇异数
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发表时间：
2010
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影响因子：
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通讯作者：
D. Tsedenbayar
中科院分区：
文献类型：
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作者：
Yu. I. Lyubich;D. Tsedenbayar
考虑了L2（0，1）中经典沃尔泰拉算子V的任意复多项式φ的谱问题（sI − φ（V）<$φ（V））f = 0.构造了一个2n阶微分方程n = deg（φ）的等价边值问题.在φ（z）= 1 + az的情形下，用超越方程的根来描述奇异数，研究了它们的局部化和渐近性态，并给出了奇异数的一个显式表达式.对于所有a6 = 0，这个范数都大于1。
The spectral problem (sI − φ(V )∗φ(V ))f = 0 for an arbitrary complex polynomial φ of the classical Volterra operator V in L2(0, 1) is considered. An equivalent boundary value problem for a differential equation of order 2n, n = deg(φ), is constructed. In the case φ(z) = 1 + az the singular numbers are explicitly described in terms of roots of a transcendental equation, their localization and asymptotic behavior is investigated, and an explicit formula for the ‖I + aV ‖2 is given. For all a 6= 0 this norm turns out to be greater than 1.