Polynomials in the de Branges spaces of entire functions |
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Authors: | Anton D Baranov |
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Institution: | (1) Department of Mathematics and Mechanics, St. Petersburg State University, 28, Universitetskii pr., St. Petersburg, 198504, Russia;(2) Laboratoire d’Analyse et Géométrie, Université Bordeaux 1, 351, Cours de la Libération, FR-33405 Talence, France |
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Abstract: | 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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Keywords: | |
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