| Convergence Of Polynomially Bounded Semigroups Of Matrices (1997) | |||||||||||||||
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| . It is proved that for polynomially bounded sets of matrices the notions of pointwise convergence and uniform convergence coincide. This result is also proved for certain sets of nonlinear maps on finite-dimensional real or complex vector spaces. Key words. uniform convergence, pointwise convergence, infinite products, matrix semigroups AMS subject classifications. 15A30, 15A99 PII. S089547989528939X 1. Introduction. Let A be a set of n × n matrices with complex or real entries. Various notions concerning convergence of infinite products of matrices in A have been studied extensively in the literature. We mention [DL2, BW, DL1], where right-convergent product sets are studied (such sets appear in many applications, for example, in constructing wavelets with compact support; see the bibliography in [DL1]). Various notions of stability of discrete linear inclusions lead to a study of infinite products of matrices and their convergence (see [G]). We also mention [S, SU], where a n... | |||||||||||||||
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