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We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The connections to the classical elastic models are also provided. Mathematics Subject Classification.doi:10.1051/m2an/2010040 fatcat:sofyzqv3ifdhhe4rsrofqq4uye