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.
Alpay, D., Paiva, I.L. & Struppa, D.C. Integr. Equ. Oper. Theory (2019) 91: 8. https://doi.org/10.1007/s00020-019-2506-6