广义Gelfand公式联合谱半径的显式先验估计
On explicit a priori estimates of the joint spectral radius by the generalized Gelfand formula
摘要：
在控制理论、非自治多值动力系统、小波理论等数学领域的各种问题中，关于矩阵集合因子积的增长率的信息起着关键作用。表征基质产物的指数增长率的最显著的量之一是所谓的联合或广义谱半径。本文利用广义Gelfand公式得到了联合谱半径的一些显式先验估计。这些估计是基于A. Pokrovskii和作者。
英文摘要：
In various problems of control theory, non-autonomous and multivalued dynamical systems, wavelet theory and other fields of mathematics information about the rate of growth of matrix products with factors taken from some matrix set plays a key role. One of the most prominent quantities characterizing the exponential rate of growth of matrix products is the so-called joint or generalized spectral radius. In the work some explicit a priori estimates for the joint spectral radius with the help of the generalized Gelfand formula are obtained. These estimates are based on the notion of the measure of irreducibility (quasi-controllability) of matrix sets proposed previously by A. Pokrovskii and the author.
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