Subnormality and moment problemsy

Abstract

There exists a strong connection between the concept of (sub)normality and that of moment problem. They interact very often, sometimes in a subtle, unexpected way. It is possible to use a (sub)normality result, providing eventually a spectral measure, used to solve a moment problem. Conversely, there are situations when the solution to a momento problem leads to the existence of a normal extension for some operators. The present work endeavor to present several results sustaining the interplay mentioned above, as well as the necessary background to understand those phenomena, both is a bounded or a unbounded context.