Algebraic spectral synthesis and crystal rigidity

Kastis, Eleftherios Michail and Power, Stephen Charles (2019) Algebraic spectral synthesis and crystal rigidity. Journal of Pure and Applied Algebra, 223 (11). pp. 4954-4965. ISSN 0022-4049

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Abstract

A spectral synthesis property is obtained for closed shift-invariant subspaces of vector-valued functions on the lattice Z^d. This result generalises Marcel Lefranc's 1958 theorem for scalar-valued functions. Applications are given to homogeneous systems of multi-variable vector-valued discrete difference equations and to the first-order flexibility of crystallographic bar-joint frameworks.