This monograph deals with the mathematics of extending given partial data-sets obtained from
experiments Experimentalists frequently gather spectral data when the observed data is limited
e.g. by the precision of instruments or by other limiting external factors. Here the limited
information is a restriction and the extensions take the form of full positive definite
function on some prescribed group. It is therefore both an art and a science to produce solid
conclusions from restricted or limited data. While the theory of is important in many areas of
pure and applied mathematics it is difficult for students and for the novice to the field to
find accessible presentations which cover all relevant points of view as well as stressing
common ideas and interconnections. We have aimed at filling this gap and we have stressed
hands-on-examples.
