9 October 2007 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 L2 0 1 Incidentally in response to the request for examples L2 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 L2 functions on the circle is not a RKHS On the other hand the space of L2 functions on the circle which are tangential limits of holomorphic functions on the disc is 14 18