Structural analysis of certain linear operators representing chemical network systems via the existence and uniqueness theorems of spectral resolution. V

The present Part V of this series of articles is devoted to the initial dev elopment of the theory of generalized repeat space for a study of the corre lation between the structure and properties in molecules having many identi cal moieties. An element of generalized repeat space, referred to as a gene ralized repeat sequence, is a d-dimensional generalization of a complex mat rix version of repeat sequence, which we studied in Part IV of this series of articles. The generalized repeat space, which satisfies the axioms of a complex *-algebra, is a far-reaching extension of the original repeat space , and we present here the fundamental theorems as an initial step toward th e formation of the theory of the generalized repeat space. (C) 1999 John Wi ley & Sons, Inc.