Resumen de A problem on completeness of exponentials

Alexei Poltoratski

• Let µ be a finite positive measure on the real line. For a>0 , denote by E a the family of exponential functions E a ={e ist |s?[0,a]}.

  The exponential type of µ is the infimum of all numbers a such that the finite linear combinations of the exponentials from E a are dense in L 2 (µ) . If the set of such a is empty, the exponential type of µ is defined as infinity. The well-known type problem asks to find the exponential type of µ in terms of µ . In this note we present a solution to the type problem and discuss its relations with known results.