Material response of passive media to external influences is described by complex analytic functions of frequency that can always be written in terms of Stieltjes functions -- a special class of analytic functions mapping complex upper half-plane into itself. Reconstructing such functions from their experimentally measured values at specific frequencies is one of the central problems that we address in this paper. A definitive reconstruction algorithm that produces a certificate of optimality as well as a graphical representation of the uncertainty of reconstruction is proposed. Its effectiveness is demonstrated in the context of the electrochemical impedance spectroscopy.
翻译:被动介质对外部影响的物质反应被描述为频率的复杂分析功能,这些功能总是可以用Stieltjes的功能写成 -- -- 一种特殊的分析功能类别,对复杂的上半空飞机进行测绘,从在特定频率实验测量的数值中重新构建这些功能,是我们在本文件中处理的中心问题之一。 提出了一个明确的重建算法,产生最佳性证明,并用图形表示重建的不确定性。 其有效性在电化学阻力光谱分析中得到了证明。