Determination of subrepresentations of the standard higher dimensional shearlet group

Document Type : Research Paper

Authors

Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran.

10.22072/wala.2017.23366

Abstract

‎This paper is devoted to definition standard higher dimension shearlet group $ \mathbb{S} = \mathbb{R}^{+} \times \mathbb {R}^{n-1} \times \mathbb {R}^{n} $ and determination of square integrable subrepresentations of this group‎. ‎Also we give a characterisation of admissible vectors associated to the Hilbert spaces corresponding to each su brepresentations‎.

Keywords

References

[1] S.T. Ali, J.P. Antoine and J.P. Gazeau, Coherent States, Wavelets and Their Generalizations, New York: Springer-Verlag, 2000.
[2] A.A. Arefijamaal and R.A. Kamyabi-Gol, A characterization of square-integrable representations associated with CWT, J. Sci., Islam. Repub. Iran, 18(2) (2007), 159-166.
[3] V. Atayi and R.A. Kamyabi-Gol, On the characterization of subrepresentations of shearlet group, Wavelets and Linear Algebra, 2(1) (2015), 1-9.
[4] D. Bernier and K.F. Taylor, Wavelet from square-integrable representation, SIAM J. Math. Anal., 27(2) (1996), 594-608.
[5] E.J. Candes and D.L. Donoho, Curvelets: A surprisingly effective nonadaptive representation for objects with edges, Saint-Malo Proceedings, 2000.
[6] E.J. Candes and D.L. Donoho, Ridgelets: a key to higher-dimensional intermittency, Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci., 357(1760) (1999), 2495-2509.
[7] S. Dahlke, G. Kutyniok, C. Sagiv, H.G. Stark and G. Teschke, The uncertainty principle associated with the continuous shearlet transform, Int. J. Wavelets Multiresolut. Inf. Process., 6(2) (2008), 157-181.
[8] S. Dahlke and G. Teschke, The continuous shearlet transform in arbitrary space dimensions, J. Fourier Anal. Appl., 16 (2010), 340-364.
[9] M.N. Do and M. Vetterli, The contourlet transform: an efficient directional multiresolution image representation, IEEE Trans. Image Process., 14(12) (2005), 2091-2106.
[10] G.B. Folland, A Course in Abstract Harmonic Analysis, Boca Katon: CRC Press, 1995.
[11] K. Guo and D. Labate, Optimally sparse multidimensional representation using shearlets, SIAM J. Math. Anal., 39(1) (2007), 298-318.
[12] K. Guo, G. Kutyniok and D. Labate, Sparse multidimensional representations using anisotropic dilation and shear operators, International Conference on the Interaction between Wavelets and Splines, Athens, 2005.
[13] E. Hewitt and K.A. Ross, Abstract Harmonic Analysis, vol. 1, Springer-Verlag, Berlin, 1963.
[14] G. Kutyniok and W. Lim, Compactly Supported Shearlets, vol. 13, Approximation Theory XIII: San Antonio 2010. Springer Proceedings in Mathematics, Springer, New York, 2011.
[15] G. Kutyniok, W. Lim and X. Zhuang, Digital shearlet transforms, Appl. Comput. Harmon. Anal., (2012), 239--282.
[16] D. Labate, W. Lim, G. Kutyniok and G. Weiss, Sparse multidimensional representation using shearlets, SPIE Proc. 5914, SPIE, Bellingham, (2005), 254-262.
Wavelet and Linear Algebra
Volume 4, Issue 1
Spring - Summer
2017
Pages 11-21

Files

Share

How to cite

Statistics