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Consider the group algebra L1(Rn).For a closed subset E of Rn,let J(E)and k(E)be the smallest and the largest closed ideals of L1(Rn)with hull E,and S ={x∈Rn : ‖x‖ = 1} the unit sphere of Rn.If J(E)= k(E),the set E is said to be a set of synthesis.In this talk I will present a series of new/recent results about the following classical theorems and answer the following questions.