# DISTANCE BETWEEN CONTINUOUS FRAMES IN HILBERT SPACE

• Amiri, Zahra (Department of Pure Mathematics Ferdowsi University of Mashhad) ;
• Kamyabi-Gol, Rajab Ali (Department of Pure Mathematics Ferdowsi University of Mashhad Center of Excellence in Analysis on Algebraic Structures (CEAAS))
• Published : 2017.01.01

#### 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.

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