3.8 .

(a) If ????(s, t) is an ordinary continuous positive semidefinite function, show that

????G(????, ????) = ∫ ????(s) ????(t) ????(s, t) ds dt defines a positive semidefinite generalized bilinear functional.

(b) If {X(t)} is an ordinary random field with covariance function ????(s, t), show that it can also be viewed as a generalized random field XG(????) =

∫ ????(t) X(t) dt with covariance functional ????G(????, ????).