SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1884-1902, January 2020.
In the paper we consider the linear inverse problem that consists in recovering the initial state in a first order evolution equation generated by a skew-adjoint operator. We studied the well-posedness of the inversion in terms of the observation operator and the spectra of the skew-adjoint generator. The stability estimate of the inversion can also be seen as a weak observability inequality. The proof of the main results is based on a new resolvent inequality and Fourier transform techniques which are of interest in themselves.

中文翻译：

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具有偏伴随发生器的演化系统的弱可观性

SIAM数学分析杂志，第52卷，第2期，第1884-1902页，2020
年1月。在本文中，我们考虑了线性逆问题，该问题涉及用偏向伴随算子生成的一阶演化方程恢复初始状态。我们根据观测算子和偏斜伴随发生器的频谱研究了反演的适定性。反演的稳定性估计也可以看作是弱的可观测性不等式。主要结果的证明是基于一种新的可分辨不等式和他们感兴趣的傅立叶变换技术。