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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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참고문헌 (15)
참고문헌 신청
A. A. Arefijamaal / 2013 / A new approach to continuous riesz bases / J. Sci. I. R. Iran 24 : 63 ~ 69
G. B. Folland / 1995 / A Course in Abstract Harmonic Analysis / CRC Press
G. Kaiser / 1994 / A Friendly Guide to Wavelets / Birkhauser
G. Kutyniok / 2005 / Sparse multidimensional represen-tation using shearlets / Wavelets XI : 254 ~ 262
G. Kutyniok / 2007 / Construction of regular and irregular shearlet frames / J. Wavelet Theory Appl 1 : 1 ~ 12
G. B. Folland / 1995 / A Course in Abstract Harmonic Analysis / CRC Press
G. Kaiser / 1994 / A Friendly Guide to Wavelets / Birkhauser
G. Kutyniok / 2005 / Sparse multidimensional represen-tation using shearlets / Wavelets XI : 254 ~ 262
G. Kutyniok / 2007 / Construction of regular and irregular shearlet frames / J. Wavelet Theory Appl 1 : 1 ~ 12
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