Rocky Mountain Journal of Mathematics

Some constructions of $K$-frames and their duals

Fahimeh Arabyani Neyshaburi and Ali Akbar Arefijamaal

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$K$-frames, as a new generalization of frames, have important applications, especially in sampling theory, to help us to reconstruct elements from a range of a bounded linear operator $K$ in a separable Hilbert space. In this paper, we focus on the reconstruction formulae to characterize all $K$-duals of a given $K$-frame. Also, we give several approaches for constructing $K$-frames.

Article information

Rocky Mountain J. Math., Volume 47, Number 6 (2017), 1749-1764.

First available in Project Euclid: 21 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42C15: General harmonic expansions, frames
Secondary: 41A58: Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)

$K$-frames $K$-duals $K$-minimal frames


Neyshaburi, Fahimeh Arabyani; Arefijamaal, Ali Akbar. Some constructions of $K$-frames and their duals. Rocky Mountain J. Math. 47 (2017), no. 6, 1749--1764. doi:10.1216/RMJ-2017-47-6-1749.

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