5.1 The spherical scheme is defined by the covariance function

????(h; ????2

,

a) = {

1 − 3 2

|h∕a| + 1 2

|h∕a|

3, |h| ≤ a, 0, |h| > a, which is positive definite in dimensions d = 1, 2, 3. The parameters are the scale parameter ????2 and the range parameter

a. Clearly, ????(h) is smooth in ????2, but its dependence on a is more delicate. Show that for fixed h ≠ 0,

(a) ????(h; ????2,

a) is continuous in a for all a > 0.

(b) ????????(h; ????2, a)∕????a is continuous in a for all a > 0.

(c) ????2????(h; ????2, a)∕????a2 is not continuous in a at a = |h|.