Geodesic
Localization Operators for Ridgelet Transforms
J. Li1 ; M. W. Wong1
1 Department of Mathematics and Statistics, York University 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada
Mathematical modelling of natural phenomena, Tome 9 (2014) no. 5, pp. 194-203.

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We prove that localization operators associated to ridgelet transforms with Lp symbols are bounded linear operators on L2(Rn). Operators closely related to these localization operators are shown to be in the trace class and a trace formula for them is given.
DOI : 10.1051/mmnp/20149513

J. Li 1 ; M. W. Wong 1

1 Department of Mathematics and Statistics, York University 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada 
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J. Li; M. W. Wong. Localization Operators for Ridgelet Transforms. Mathematical modelling of natural phenomena, Tome 9 (2014) no. 5, pp. 194-203. doi : 10.1051/mmnp/20149513. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20149513/

[1] E. J. Candès. Ridgelets: Theory and Applications. Ph.D. Thesis, Department of Statistics, Stanford University, 1998.

[2] E. J. Candès, D. L. Donoho R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci. 1999 2495 2509

[3] E. J. Candès, D. L. Donoho Appl. Comput. Harmon. Anal. 2005 198 222

[4] V. Catan\hbox{${\rm \breve{a}}$}˘a. Products of two-wavelet multipliers and their traces. in Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations, Operator Theory: Advances and Applications 205, Birkhäuser, 2010, 195–211.

[5] I. Daubechies IEEE Trans. Inform. Theory 1988 605 612

[6] I. Daubechies. Ten Lectures on Wavelets, SIAM, 1992.

[7] J. Du, M. W. Wong C. R. Math. Rep. Acad. Sci. Canada 2001 148 152

[8] P. Goupillaud, A. Grossmann, J. Morlet Geoexploration 1984 85 102

[9] Z. He, M. W. Wong J. Austral. Math. Soc. Ser. B 1999 437 446

[10] H. J. Landau, H. O. Pollak Bell Syst. Tech. J. 1961 65 84

[11] J. Li, M. W. Wong J. Pseudo-Differ. Oper. Appl. 2012 121 143

[12] V. B. Lidskii Dokl. Akad. Nauk SSR 1959 485 487

[13] H. J. Pollak Bell Syst. Tech. J. 1962 1295 1336

[14] D. Slepian Proc IEEE 1976 292 300

[15] D. Slepian SIAM Rev. 1983 379 393

[16] D. Slepian, H. O. Pollak Fourier analysis and uncertainty, I, Bell Syst. Tech. J. 1961 43 64

[17] E. M. Stein, R. Shakarchi. Fourier Analysis: An Introduction. Princeton University Press, 2003.

[18] M. W. Wong. Weyl Transforms. Springer, 1998.

[19] M. W. Wong. Wavelet Transforms and Localization Operators. Birkhäuser, 2002.

[20] M. W. Wong. Discrete Fourier Analysis. Birkhäuser, 2011.

[21] M. W. Wong, Z. Zhang Integr. Equ. Oper. Theory 2002 498 503

[22] M. W. Wong, Z. Zhang Bull. London Math. Soc. 2002 739 744

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