Positivity, rational Schur functions, Blaschke factors, and other related results in the Grassmann algebra

Abstract

We begin a study of Schur analysis in the setting of the Grassmann algebra, when the latter is completed with respect to the $1$-norm. We focus on the rational case. We start with a theorem on invertibility in the completed algebra, and define a notion of positivity in this setting. We present a series of applications pertaining to Schur analysis, including a counterpart of the Schur algorithm, extension of matrices and rational functions. Other topics considered include Wiener algebra, reproducing kernels Banach modules, and Blaschke factors.

arXiv comment35 pages

References in corpus (1)

• Distribution spaces and a new construction of stochastic processes associated with the Grassmann algebra

Cited by in corpus (2)

• Supergroup Structure of Jackiw-Teitelboim Supergravity
• Generalized Grassmann algebras and applications to stochastic processes