Recall the bump basis {n(t)}Nn =1 from Homework 2, Problem 2, n(t) = g(Nt n 1/2), g(t) = et2 . Call its span TN equip it with the standard inner product. This is a finite dimensional Hilbert space, and so it an RKHS. In this problem, we will generate the reproducing kernel. 1 Last updated 12:15, September 22, 2023 (a) Fix R. Show that if we have a k TN that obeys n, k = n( ) for n = 1, . . . ,N then f, k = f( ) for all f TN. (b) Since k TN, there is a RN such that k = PN n=1 nn. Show how we can set up a set of linear equations to solve for the