Upper bounds for the derivative of exponential sums Academic Article

The equality [ /mml:mo> p | p ( a ) | p [ a , b ] = 2 n 2 b a sup limits _p frac {{|p(a)|}}{{{{left | p
ight |}_{[a,b]}}}} = frac {{2{n^2}}}{{b - a}} ] is shown, where the supremum is taken for all exponential sums p of the form [ p ( t ) = a 0 + j = 1 n a j e j t , a j R , p(t) = {a_0} + sum limits _{j = 1}^n {{a_j}{e^{{lambda _j}t}},quad {a_j} in {mathbf {R}},} ] with nonnegative exponents j {lambda _j} . The inequalities [ <