Delta function in Matlab

In image de-blurrring processs, PSF(h) is first asssumed to be a delat function, i.e 1 for pixel

but sum(h(x,y))=1, h(x,y)>=0, are the conditions/ contraints for psf.

considering the first constraint ,each pixcel cannot be alloted 1, i am confused, can anyone guide me regarding the delta-function.