REMARKS ON RESOLUTIONS OF HILBERT-SCHMIDT OPERATORS

A generalization due to All, Antoine, and Gazeau of the notion of square integrability of representations is used to construct operators as integrals over compact homogeneous spaces X=G/H. It is shown that such operators are Hilbert-Schmidt, and a formula for the Hilbert-Schmidt norm is given. Finally, two examples are given demonstrating the dependence of the Hilbert-Schmidt norm on the section cr: X-->G used to construct it. One example, involving the three-dimensional Euclidean group, makes interesting use of Bessel coefficients. (C) 1995 American Institute of Physics.