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Sampling and interpolation in de Branges spaces with doubling phase

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Author

Summary, in English

The de Branges spaces of entire functions generalize the classical Paley-Wiener space of square summable bandlimited functions. Specifically, the square norm is computed on the real line with respect to weights given by the values of certain entire functions. For the Paley-Wiener space, this can be chosen to be an exponential function where the phase increases linearly. As our main result, we establish a natural geometric characterization in terms of densities for real sampling and interpolating sequences in the case when the derivative of the phase function merely gives a doubling measure on the real line. Moreover, a consequence of this doubling condition is that the spaces we consider are model spaces generated by a one-component inner function. A novelty of our work is the application to de Branges spaces of techniques developed by Marco, Massaneda and Ortega-CerdA for Fock spaces satisfying a doubling condition analogous to ours.

Publishing year

2012

Language

English

Pages

365-395

Publication/Series

Journal d'Analyse Mathematique

Volume

117

Issue

1

Document type

Journal article

Publisher

Magnes Press

Topic

  • Mathematics

Status

Published

ISBN/ISSN/Other

  • ISSN: 1565-8538