Structure Of the Truncated Laurent's Series Space as An Extension of Fuhrmann's Bilinear Form

Abstract

The behavior of the Fuhrmann dynamic systems is a closed subspace of the truncated Laurent series space, thus it can be concluded that the stability of the dynamic systems can be related to the closed nature of the behavior system studied. Since the behavior of a dynamic systems is a closed subspace of the truncated Laurent series space, this fact provides inspiration to study the characteristics of the truncated Laurent series space, especially related to the development of the Fuhrmann’s bilinear form into a k-bilinear form, the structure of the closed subspace in the truncated Laurent’s series space and the condition that satisfy Riesz representation theorem in truncated Laurent’s series space.