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The algebraic structure of linearly recursive sequences under hadamard product

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Abstract

We describe the algebraic structure of linearly recursive sequences under the Hadamard (point-wise) product. We characterize the invertible elements and the zero divisors. Our methods use the Hopf-algebraic structure of this algebra and classical results on Hopf algebras. We show that our criterion for invertibility is effective if one knows a linearly recursive relation for a sequence and certain information about finitely-generated subgroups of the multiplicitive group of the field.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Chicago, 60680, Chicago, IL, USA

    Richard G. Larson

  2. Department of Mathematics, Rutgers University, 08903, New Brunswick, NJ, USA

    Earl J. Taft

Authors
  1. Richard G. Larson
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  2. Earl J. Taft
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Supported in part by NSF Grant DMS 870-1085.

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Larson, R.G., Taft, E.J. The algebraic structure of linearly recursive sequences under hadamard product. Israel J. Math. 72, 118–132 (1990). https://doi.org/10.1007/BF02764615

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  • DOI: https://doi.org/10.1007/BF02764615

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