october utc p s the delta function i use in the example above as is the kronecker delta not the dirac delta the kronecker delta is in whereas the dirac delta is not in l incidentally in response to the request for examples l x is not a rkhs for x any open subset of on the other hand hardy spaces usually are rkhss using various variants of the szego kernel for example the hilbert space of l functions on the circle is not a rkhs on the other hand the space of l functions on the circle which are tangential limits of holomorphic functions on the disc is