Georgia Institute of Technology College of Sciences

One of the basic problems of Harmonic analysis is to determine ifa given collection of functions is complete in a given Hilbert space. Aclassical theorem by Beurling and Malliavin solved such a problem in thecase when the space is $L^2$ on an interval and the collection consists ofcomplex exponentials. Two closely related problems, the so-called Gap andType Problems, studied by Beurling, Krein, Kolmogorov, Levinson, Wiener andmany others, remained open until recently.In my talk I will  present solutions to the Gap and Type problems anddiscuss their connectionswith adjacent fields.