关于线性系理论中的Carleson测度准则
On the Carleson measure criterion in linear systems theory
摘要：
在Ho，Russell和Weiss中，给出了一维输入元关于对角半群的容许性的Carleson测度准则。我们将他们的结果从希尔伯特空间情形$X=\ell_2$和$L^2$ --容许性推广到更一般的情形$L^p$ --容许性在$\ell_q$ --空间上.在解析对角半群的情形下，我们给出了一个不依赖于拉普拉斯变换方法的新结果。通过对这两个判据的比较，得到了$L^p$ --倒易系统在Curtain意义下的容许性.
英文摘要：
In Ho, Russell, and Weiss, a Carleson measure criterion for admissibility of one-dimensional input elements with respect to diagonal semigroups is given. We extend their results from the Hilbert space situation $X=\ell_2$ and $L^2$--admissibility to the more general situation of $L^p$--admissibility on $\ell_q$--spaces. In case of analytic diagonal semigroups we present a new result that does not rely on Laplace transform methods. A comparison of both criteria leads to result of $L^p$--admissibility for reciprocal systems in the sense of Curtain.
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