Designing a regression experiment in Hilbert space

Two forms of a priori information about unknown parameters in observing linear regression with noise in a Hilbert space are considered. In each section one gets best restricted linear unbiased estimates of the unknown parameters generalizing known results about the finite-dimensional case. Problems of choice of optimal designs are solved for bounded closed sets which are natural from the point of view of applications. The results are compared with those which hold without a priori information.Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 23–28, 1988.