Exponents of operator self-similar random fields

If X(cEt) and cHX(t) have the same finite-dimensional distributions for some pair of linear operators E and H, we say that the random vector field X(t) is operator self-similar. The exponents E and H are not unique in general, due to symmetry. This paper characterizes the possible set of range exponents H for a given domain exponent, and conversely, the set of domain exponents E for a given range exponent.