On the correspondence between subspace collections and Herglotz functions

The response of many passive linear physical systems are governed by Herglotz or Stieltjes functions. Typically associated with these functions is some sort of Hilbert space, or in the case of composites, a subspace collection. Operations on Herglotz or Stieltjes function often have a parallel operation on subspace collections. Here we will explore this correspondence. Also we give representation formulas for the effective (conductivity, elastic, piezoelectric, etc.) properties of two-dimensional composites of two anisotropic phases.Non UBCUnreviewedAuthor affiliation: University of UtahFacult