I have been reading about moment problem and I have been curious about the following question. 


What is the motivation for studying the Hamburger moment problem(one dimensional moment problem? 


I have been asking myself out of curiosity, what is gained by people who considered this case? or let me say how can I explain my reasons to someone who has little knowledge about the subject the reasons for for studying hamburger moment problem.


I will be more than happy if useful literatures can be suggested or provided with some explanations.


Thanks for your useful suggestions and explanations.



Why study the moment problem in one dimensional case( Hamburger moment problem)
It has many applications, especially in probability: e.g. you want to know if there is a probability distribution satisfying some condition on its moments.
Or you know the moments of a random variable match those of a certain distribution, and you want to know if that implies this is the distribution of the random variable.


I'm not claiming this as a major motivation, but [one of my papers](http://projecteuclid.org/euclid.cmp/1103904299) happens to contain an application of the Hamburger moment problem to mathematical physics: 
a characterization of reflection positivity for pair interactions in one-dimensional lattice systems (see Prop. 3.2).


