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 development of the theory of generalized repeat space for a study of the correlation between the structure and properties in molecules having many identical moieties. An element of generalized repeat space, referred to as a generalized repeat sequence, is a d-dimensional generalization of a complex matrix 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 the formation of the theory of the generalized repeat space. (C) 1999 John Wiley & Sons, Inc.