Continuous $ k $-Frames and their Dual in Hilbert Spaces

Authors

  • Gholamreza Rahimlou Department of Mathematics, Shabestar Branch,Islamic Azad University, Shabestar, Iran.
  • Reza Ahmadi Institute of Fundamental Science, University of Tabriz, Tabriz, Iran.
  • Susan Nami Faculty of Physic, University of Tabriz, Tabriz, Iran.
Abstract:

The notion of $k$-frames was recently introduced by Gu avruc ta in Hilbert  spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$-frame, so called c$k$-frame along with an atomic system for this version of frames. Also we introduce a new method for obtaining the dual of a c$k$-frame and prove some new results about it.

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Journal title

volume 17  issue 3

pages  145- 160

publication date 2020-07-01

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