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Abstract
K -frames are strong tools for the reconstruction of elements from range of a bounded linear operator K on a separable Hilbert space H. In this paper, we study some properties of K -frames and introduce the K -frame multipliers. We also focus on representing elements from the range of K by K -frame multipliers.
Highlights
K -frames are strong tools for the reconstruction of elements from range of a bounded linear operator K on a separable Hilbert space H
Frames in Hilbert space were offered by Duffin and Schaeffer in 1952 and were brought to life by Daubechies et al [18]
This fact has a key role in applications such as signal processing, image processing, coding theory, and more
Summary
Definition 2.2 Let {fi}i∈I be a Bessel sequence. A Bessel sequence {gi}i∈I ⊆ H is called a K -dual of {fi}i∈I if. An approach to the K -duals of a K -frame can be found in [1]. Notice that K -duals of [1] satisfy (2.3). The K -duals introduced by (2.3) covers a larger class than the K -duals of [1]. Lemma and BG , 2.3 [1] If G respectively
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