Will a smartphone, bought in the USA work in Belgium?

Recently, the Google Nexus 5 (smartphone) has been released. Unfortunately the price in Europe for the basic model is €400 (=$540) while the price in the USA is $350 thats a difference of $140...

So I was wondering, could I buy the device in the USA and use the device in Belgium without having any limitations or warranty problems. I have been trying to find this on google but I couldn't really find much about this topic.

thanks in advance

Nexus 5 | http://www.google.com/nexus/5/