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arXiv · 1810.02843

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

Daniel Alpay·Ismael L. Paiva·Daniele C. Struppa
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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.

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Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa. 2018-10-05. Positivity, rational Schur functions, Blaschke factors, and other related results in the Grassmann algebra. https://doi.org/10.1007/s00020-019-2506-6

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