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

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

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish
Article number8
JournalIntegral Equations and Operator Theory
Volume91
Issue number2
DOIs
StatePublished - 1 Apr 2019
Externally publishedYes

Keywords

  • Grassmann algebra
  • Schur analysis
  • Toeplitz matrices
  • Wiener algebra

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