Polynomials in the de Branges spaces of entire functions

Anton D. Baranov Department of Mathematics and Mechanics, St. Petersburg State University

TBD mathscidoc:1701.333077

Arkiv for Matematik, 44, (1), 16-38, 2004.11
We study the problem of density of polynomials in the de Branges spaces ℋ($E$) of entire functions and obtain conditions (in terms of the distribution of the zeros of the generating function$E$) ensuring that the polynomials belong to the space ℋ($E$) or are dense in this space. We discuss the relation of these results with the recent paper of V. P. Havin and J. Mashreghi on majorants for the shift-coinvariant subspaces. Also, it is shown that the density of polynomials implies the hypercyclicity of translation operators in ℋ($E$).
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  title={Polynomials in the de Branges spaces of entire functions},
  author={Anton D. Baranov},
  booktitle={Arkiv for Matematik},
Anton D. Baranov. Polynomials in the de Branges spaces of entire functions. 2004. Vol. 44. In Arkiv for Matematik. pp.16-38. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203616677606886.
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