INGHAM TYPE THEOREMS AND GAP CONDITIONS
Paola Loreti · 2007
We recall a classical theorem due to Ingham (1936)[1]: Let (λk)k∈Z be a given sequence of real numbers, and consider the functions of the form (1) f(t) = k∈Z ake iλkt with complex coefficients (ak). Theorem 1. Assume that γ: = inf j 6=k |λj − λk |> 0 gap condition, and let I be a bounded interval of length |I |> 2pi/γ. There exist two constants c1, c2> 0 such that c1 k