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On the properties of generalized frames

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Abstract

In this paper, we introduce the notion of generalized frames and study their properties. Discrete and integral frames are special cases of generalized frames. We give criteria for generalized frames to be integral (discrete). We prove that any bounded operator A with a bounded inverse acting from a separable space H to L 2(Ω) (where Ω is a space with countably additive measure) can be regarded as an operator assigning to each element x ∈ H its coefficients in some generalized frame.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. A. Zakharova

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  1. A. A. Zakharova
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Correspondence to A. A. Zakharova.

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Original Russian Text © A. A. Zakharova, 2008, published in Matematicheskie Zametki, 2008, Vol. 83, No. 2, pp. 210–220.

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Zakharova, A.A. On the properties of generalized frames. Math Notes 83, 190–200 (2008). https://doi.org/10.1134/S0001434608010215

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  • DOI: https://doi.org/10.1134/S0001434608010215

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