Document Type

Article

Publication Date

2-13-2019

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.

Comments

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.

Online access to this article has been shared by the author(s) via Springer Nature SharedIt. Please click here to read a free version of this article.

Peer Reviewed

1

Copyright

Springer

Available for download on Thursday, February 13, 2020

Included in

Algebra Commons

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