Consider the following classic result from real analysis. Let {fn(t) : t ∈ [0, 1], n = 1, 2, . . . } be a sequence of functions that (1) converges point-wise to a function f(t) and (2) has derivatives...

Consider the following classic result from real analysis. Let {fn(t) : t ∈ [0, 1], n = 1, 2, . . . } be a sequence of functions that (1) converges point-wise to a function f(t) and (2) has derivatives {f 0 n (t)} that are uniformly convergent to a function g. Then it must be the case that f 0 = g. a) Use the above result to show that the RKHS generated by the Gaussian kernel (Example 7.2.2) consists of functions which are at least one time continuously differentiable. Use the fact that every element of the RKHS can be expressed as

b) Briefly explain why the RKHS for the exponential kernel contains functions which need not be differentiable.