Positivity, Rational Schur Functions, Blaschke Factors, and Other Related Results in the Grassmann Algebra

Authors

Daniel Alpay, Chapman UniversityFollow
Ismael L. Paiva, Chapman UniversityFollow
Daniele C. Struppa, Chapman UniversityFollow

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.

Recommended Citation

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

Peer Reviewed

1

Copyright

Springer