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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.


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Integral Equations and Operator Theory, volume 91, in 2019 following peer review. The final publication is available at Springer via DOI: 10.1007/s00020-019-2506-6.

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