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Generic Fréchet differentiability of the pressure in certain lattice systems

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Abstract

This note has two goals. The first is to give an explicit description (Theorem 1) of the duals of certain weighted products ℛ h of a countable family of Banach spaces. These products include the usual spaces of interactions which arise in statistical mechanics. The second goal is to use this description to prove that if the factor spaces are finite dimensional and the weight functionh satisfies a certain growth condition, then the pressure is Fréchet differentiable wherever it is Gateaux differentiable (hence is Fréchet differentiable in a denseG δ subset).

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Authors and Affiliations

  1. Department of Mathematics GN-50, University of Washington, 98195, Seattle, WA, USA

    R. R. Phelps

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  1. R. R. Phelps
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Communicated by J. Fröhlich

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Phelps, R.R. Generic Fréchet differentiability of the pressure in certain lattice systems. Commun.Math. Phys. 91, 557–562 (1983). https://doi.org/10.1007/BF01206022

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  • DOI: https://doi.org/10.1007/BF01206022

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