Nonexistence results for relaxation spectra with compact support
Nonexistence results for relaxation spectra with compact support
复制标题
具有紧凑支撑的弛豫谱不存在结果
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
H. Gruffudd
中科院分区：
文献类型：
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作者：
R. Douglas;H. Gruffudd
本文考虑了通过反演积分方程g = sech？h？>，在哪里？>表示卷积，使用傅立叶变换。我们特别感兴趣的是建立h的属性，假设g的傅立叶变换具有复平面的整个扩展。在平方可积函数的情况下，我们证明了Paley-Wiener定理不能用来证明具有紧支集的非平凡松弛谱的存在性。我们证明了一个更强的结果回火分布：有没有非平凡的松弛谱紧支持。最后给出了弛豫谱h严格正定的充要条件。
In this paper we consider the problem of recovering the (transformed) relaxation spectrum h from the (transformed) loss modulus g by inverting the integral equation g = sech ∗ h ?> , where ∗ ?> denotes convolution, using Fourier transforms. We are particularly interested in establishing properties of h, having assumed that the Fourier transform of g has entire extension to the complex plane. In the setting of square integrable functions, we demonstrate that the Paley–Wiener theorem cannot be used to show the existence of non-trivial relaxation spectra with compact support. We prove a stronger result for tempered distributions: there are no non-trivial relaxation spectra with compact support. Finally we establish necessary and sufficient conditions for the relaxation spectrum h to be strictly positive definite.