GEOMETRIC ASPECTS OF MULTIPARAMETER SPECTRAL THEORY

The paper contains a geometric description of the dimension of the tot al root subspace of a regular multiparameter system in terms of the in tersection multiplicities of its determinantal hypersurfaces. The new definition of regularity used here is proved to restrict to the famili ar definition in the linear case. A decomposability problem is also co nsidered. It is shown that the joint root subspace of a multiparameter system may be decomposable even when the root subspace of each member is indecomposable.