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

  • Daniel AlpayEmail author
  • Ismael L. Paiva
  • Daniele C. Struppa


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.


Grassmann algebra Schur analysis Wiener algebra Toeplitz matrices 

Mathematics Subject Classification

30G35 15A75 47S10 



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Authors and Affiliations

  1. 1.Schmid College of Science and TechnologyChapman UniversityOrangeUSA
  2. 2.Donald Bren Distinguished Presidential Chair in MathematicsChapman UniversityOrangeUSA

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