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Multi-orbital Frames Through Model Spaces

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Abstract

We characterize the normal operators A on \(\ell ^2\) and the elements \(a^i \in \ell ^2\), with \(1\le i\le m\), such that the sequence

$$\begin{aligned} \{ A^n a^1, \ldots , A^n a^m \}_{n\ge 0} \end{aligned}$$

is a frame. The characterization makes strong use of the pseudo-hyperbolic metric of \( {{\mathbb {D}}} \) and is given in terms of the backward shift invariant subspaces of \(H^2( {{\mathbb {D}}} )\) associated to finite products of interpolating Blaschke products.

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Authors and Affiliations

  1. The Department of Mathematics, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina

    Carlos Cabrelli, Ursula Molter & Daniel Suárez

  2. IMAS-CONICET-UBA, Buenos Aires, Argentina

    Carlos Cabrelli & Ursula Molter

  3. IAM-CONICET, Buenos Aires, Argentina

    Daniel Suárez

Authors
  1. Carlos Cabrelli
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  2. Ursula Molter
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  3. Daniel Suárez
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Corresponding author

Correspondence to Ursula Molter.

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Communicated by Eric Weber.

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Supported by Universidad de Buenos Aires UBACyT 20020170100430BA, CONICET PIP11220150100355 and SECyT PICT 2014-1480.

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Cabrelli, C., Molter, U. & Suárez, D. Multi-orbital Frames Through Model Spaces. Complex Anal. Oper. Theory 15, 16 (2021). https://doi.org/10.1007/s11785-020-01063-6

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  • DOI: https://doi.org/10.1007/s11785-020-01063-6

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