I am not familiar with the formatting that you have typed so I apologize that I cannot give you a more precise answer. Although to undo a double integral "verify", you will need to Partial Differentiate. With the provided equation w(x,t)=int _0^t int_-infty^infty f(s,v)z(x-s,t-v)dsdv, we can see that you will be integrating with respect to "s" first while holding "v" as a constant. You will do the same when you differentiate; first differentiate the function as you normally would for a single variable, with respect to "s", and hold "v" as a constant. Then you do the same but with respect to "v" while holding "s" as a constant. Hope that helps...