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AbstractA topological algebra admits spectral synthesis of ideals (SSI) if every closed ideal in this algebra is an intersection of closed primary ideals. According to classical results this is the case for algebras of continuous, several times continuously differentiable, and Lipschitz functions. New examples (and counterexamples) of function algebras that admit or fail to have SSI are presented. It is shown that the Sobolev algebra , 1 ≤ p < ∞, has the property of SSI for and only for n =...
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