A problem on completeness of exponentials

• Autores: Alexei Poltoratski
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 178, Nº 3, 2013, págs. 983-1016
• Idioma: inglés
• DOI: 10.4007/annals.2013.178.3.4
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.