Distance between continuous frames in Hilbert space

Zahra Amiri; Rajab Ali Kamyabi-Gol

doi:10.4134/JKMS.j150684

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2017; 54(1): 215-225

Online first article November 15, 2016 Printed January 1, 2017

https://doi.org/10.4134/JKMS.j150684

Distance between continuous frames in Hilbert space

Zahra Amiri and Rajab Ali Kamyabi-Gol

Ferdowsi University of Mashhad, Center of Excellence in Analysis on Algebraic Structures (CEAAS)

Abstract

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Abstract

In this paper, we study some equivalence relations between continuous frames in a Hilbert space $\mathcal{H}$. In particular, we seek two necessary and sufficient conditions under which two continuous frames are near. Moreover, we investigate a distance between continuous frames in order to acquire the closest and nearest tight continuous frame to a given continuous frame. Finally, we implement these results for shearlet and wavelet frames in two examples.

Keywords: closeness bound, distance between frames, nearness

MSC numbers: Primary 43A15; Secondary 43A25, 42C15