双旋转不变Radon变换的一个等价刻画
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摘要
给出双旋转不变Radon变换的一个等价刻画.证明了双旋转不变Radon变换的双旋转不变性可以被■×■×[0,1]×■上的函数所刻画.
This paper focus on the characterization of the bi-rotation invariant Radon transforms. We proved that the bi-rotation invariant property of the bi-rotation invariant Radon transform can be characterized by a function on ■ × ■× [0,1]×■.
This paper focus on the characterization of the bi-rotation invariant Radon transforms. We proved that the bi-rotation invariant property of the bi-rotation invariant Radon transform can be characterized by a function on ■ × ■× [0,1]×■.
引文
[1] Helgason S. The Radon transform, second edition[M]. Berlin:Birkhauser, 1999.
[2] Ludwing D. The Radon transform on Euclidean space[J]. Comm Pure Appl Math, 1966, 19:49-81.
[3] Beylkin G. The invertion problem and application of the generalized Radon transform[J]. Comm Pure Appl Math, 1984, 37:579-599.
[4] Cormack A M and Quinto E T. A Radon transform on spheres through the origin in R~n and applications to the Darboux equation[J]. Trans Amer Math Soc, 1980, 260:561-575.
[5] John F. Plane waves and spherical means applied to partial differential equations[M]. New York:Interscience Publishers, 1955.
[6] Lax P D, and Philips R S. The Paley-Wiener theorem for the Radon transform[J]. Comm Pure Appl Math, 1970, 23:409-424.
[7] Rhee H. A representation of the solutions of the Darboux equation in odd-dimensional spaces[J].Trans Amer Math Soc, 1970, 150:491-498.
[8] Bai L L, and He J X. Generalized wavelets and invertion of the Radon transform on the Laguere hypergroup[J]. Approx Theory Appl, 2002, 18:55-69.
[9] Rubin B. Spherical Radon transform and related wavelet transforms[J]. Appl Comput Harmon Anal,1998, 5:202-215.
[10] Rubin B. Invertion of Radon transform using wavelet transforms generated by wavelet measures[J].Math Scand, 1999, 85(2):285-300.
[11] Keinert F. Invertion ofκ-plane transforms and applications in computer tomography[J], SIAM Rev,1989, 31:273-289.
[12] Phong D H and Stein E M. Models of degenerate Fourier integral operators and Radon transforms[J].Ann Math, 1994, 140:703-722.
[13] Solmon D C. A note onκ-plane integral transform[J]. J. Math Anal Appl, 1979, 71:351-358.
[14] Helgason S. The Radon transform on Euclidean space, compact two-point homogeneouse spaces and Grassmann manifolds[J]. Acta Math, 1965, 113:153-180.
[15] Helgason S. Geometric analysis on symmetric spaces[M]. Providence,Ri:American Mathematical Society, 1994.
[16] Nessibi M M and Trimeche K. Invertion of the Radon transform on the Lauguerre hypergroup by using generalized wavelets[J]. J Math Anal Appl, 1997, 208:337-363.
[17] Stricharz R S. L~p harmonic analysis and Radon transforms on Heisenberg Group[J]. J Func Annal,1991, 96:350-406.
[18] Ehrenpreis L. The Universality of the Radon transform[M]. New York:Oxford University Press Inc., 2003.
[19] Gelfand I M, Graev M I and Vilenkin N Y. Generalized functions, Vol. 5:integral geometry and representation theory[M]. New York:Academic Press, 1966.
[20] Natterer F. The Mathematics of Comuterized Tomography[M]. Stuttgart:John Wiley&Sons Ltd and B G Teubner, 1986.
[21] Natterer F. On the inversion of the attenuated Radon transform[J]. Numer Math, 1979, 32:431-438.
[22] Natterer F. Inversion of the attenuated Radon transform[J]. Inverse Problems, 2001,17(1):113-119.
[23] Sogge C D,and Stein E M. Averages over hypersurfaces. Smoothness of generalized Radon transforms[J]. J Analyse Math, 1990, 54:165-188.
[24] Quinto E T. The Invertibility of Rotatioa Invariant Radon Transforms[J]. J Math Anal Appl, 1983,91:510-522.
[2] Ludwing D. The Radon transform on Euclidean space[J]. Comm Pure Appl Math, 1966, 19:49-81.
[3] Beylkin G. The invertion problem and application of the generalized Radon transform[J]. Comm Pure Appl Math, 1984, 37:579-599.
[4] Cormack A M and Quinto E T. A Radon transform on spheres through the origin in R~n and applications to the Darboux equation[J]. Trans Amer Math Soc, 1980, 260:561-575.
[5] John F. Plane waves and spherical means applied to partial differential equations[M]. New York:Interscience Publishers, 1955.
[6] Lax P D, and Philips R S. The Paley-Wiener theorem for the Radon transform[J]. Comm Pure Appl Math, 1970, 23:409-424.
[7] Rhee H. A representation of the solutions of the Darboux equation in odd-dimensional spaces[J].Trans Amer Math Soc, 1970, 150:491-498.
[8] Bai L L, and He J X. Generalized wavelets and invertion of the Radon transform on the Laguere hypergroup[J]. Approx Theory Appl, 2002, 18:55-69.
[9] Rubin B. Spherical Radon transform and related wavelet transforms[J]. Appl Comput Harmon Anal,1998, 5:202-215.
[10] Rubin B. Invertion of Radon transform using wavelet transforms generated by wavelet measures[J].Math Scand, 1999, 85(2):285-300.
[11] Keinert F. Invertion ofκ-plane transforms and applications in computer tomography[J], SIAM Rev,1989, 31:273-289.
[12] Phong D H and Stein E M. Models of degenerate Fourier integral operators and Radon transforms[J].Ann Math, 1994, 140:703-722.
[13] Solmon D C. A note onκ-plane integral transform[J]. J. Math Anal Appl, 1979, 71:351-358.
[14] Helgason S. The Radon transform on Euclidean space, compact two-point homogeneouse spaces and Grassmann manifolds[J]. Acta Math, 1965, 113:153-180.
[15] Helgason S. Geometric analysis on symmetric spaces[M]. Providence,Ri:American Mathematical Society, 1994.
[16] Nessibi M M and Trimeche K. Invertion of the Radon transform on the Lauguerre hypergroup by using generalized wavelets[J]. J Math Anal Appl, 1997, 208:337-363.
[17] Stricharz R S. L~p harmonic analysis and Radon transforms on Heisenberg Group[J]. J Func Annal,1991, 96:350-406.
[18] Ehrenpreis L. The Universality of the Radon transform[M]. New York:Oxford University Press Inc., 2003.
[19] Gelfand I M, Graev M I and Vilenkin N Y. Generalized functions, Vol. 5:integral geometry and representation theory[M]. New York:Academic Press, 1966.
[20] Natterer F. The Mathematics of Comuterized Tomography[M]. Stuttgart:John Wiley&Sons Ltd and B G Teubner, 1986.
[21] Natterer F. On the inversion of the attenuated Radon transform[J]. Numer Math, 1979, 32:431-438.
[22] Natterer F. Inversion of the attenuated Radon transform[J]. Inverse Problems, 2001,17(1):113-119.
[23] Sogge C D,and Stein E M. Averages over hypersurfaces. Smoothness of generalized Radon transforms[J]. J Analyse Math, 1990, 54:165-188.
[24] Quinto E T. The Invertibility of Rotatioa Invariant Radon Transforms[J]. J Math Anal Appl, 1983,91:510-522.