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Finite dimensionality and upper semicontinuity of compact kernel sections of non-autonomous lattice systems

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  • In this paper, we first establish a criteria for finite fractal dimensionality of a family of compact subsets of a Hilbert space, and apply it to obtain an upper bound of fractal dimension of compact kernel sections to first order non-autonomous lattice systems. Then we consider the upper semicontinuity of kernel sections of general first order non-autonomous lattice systems and give an application.
    Mathematics Subject Classification: 35B40, 37L50, 35Q55.


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