Porcelain veneers look abraded and dull 3 weeks after having them placed. I don't know why. Can they be restored via polishing?

It really depends on which type of veneers you have.  If the veneers are made of composite (i.e., bonding), then it is not common at all for this type to scratch and stain very quickly.  If your veneers are porcelain, then they are likely made of emax or zirconia.  These two types are not very likely to scratch or stain easily.  If you indeed have porcelain veneers and they are scratched, I would encourage you to speak to your dentist about this issue.  It's possible that the veneers are not scratched at all, but simply have left over cement on them that is giving you a scratchy feel, when running your tongue over them.  I'm not saying that this is the case in your situation, but I'm letting you know that this is a possibility.  I hope this helps, some.Dr. Sarah ThompsonDreamDentist St. Louis, Missouri 

Hi:It would be best to post a photo of the veneers for more accurate response.  Porcelain veneers can definitely be polished to get back their shine.  Please go back to your dentist to have him look at the area to determine what exactly has happened and for a repolish.Best,Dr. Maddahi

Yes, your veneers can be polished if the glaze was adjusted off.  Newer Ceramics such as eMax will polish to a much higher luster than older porcelain which ideally needs to be glazed due to it's porous nature.