A Fast Transform for Spherical Harmonics

Journal of Fourier Analysis and Applications

Volumn 5, Issue 2-3, 1999, Pages 158-184

  Mohlenkamp, Martin J ^a,b  

^a YALE UNIVERSITY   (United States)

^b UNIVERSITY OF COLORADO   (United States)

Author keywords

Associated Legendre functions; Fast transforms; Spherical harmonics

Indexed keywords

EID: 0347511542     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf01261607     Document Type: Article

References (22)

1. Alpert, B. and Rokhlin, V. (1991). A fast algorithm for the evaluation of Legendre expansions, SIAM J. Sci. Stat. Comp., 12(1), 158-179.
2. Abramowitz, M. and Stegun, I.A. (1964). Handbook of Mathematical Functions, Vol. 55 of Applied Math Series, National Bureau of Standards.
3. Bradie, B., Coifman, R., and Grossmann, A. (1993). Fast numerical computations of oscillatory integrals related to acoustic scattering, Appl. Comp. Harmon. Anal., 1, 94-99.
4. Beylkin, G., Coifman, R., and Rokhlin, V. (1991). Fast wavelet transforms and numerical algorithms, Comm. Pure Appl. Math., 44, 141-183.
5. Bennet, N.N. (1997). Signal Analysis of Chirps: Detection, Oscillatory Kernels, and Anisotropic Wavelets, Ph.D. Thesis, Yale University, New Haven, CT.
6. Bender, C.M. and Orzag, S.A. (1978). Advanced Mathematical Methods for Scientists and Engineers, International series in pure and applied mathematics, McGraw-Hill, New York.
7. Brown, T.M. (1985). Solar rotation as a function of depth and latitude, Nature, 317(17), 591-594.
8. Coifman, R.R. and Meyer, Y. (1991). Remarques sur l'analyse de Fourier à fenêtre, C.R. Académie des Sciences, 312(1), 259-261.
9. Duvall, Jr., T.L., Elowitz, M., and Hill, F. (1989). A test of a modified algorithm for computing spherical harmonic coefficients using an fft, J. Comp. Phys., 80, 506-511.
10. Driscoll, J.R. and Healy, Jr., D.M. (1994). Computing Fourier transforms and convolutions on the 2-sphere, Adv. in Appl. Math., 15, 202-250.
11. Dilts, G.A. (1985). Computation of spherical harmonic expansion coefficients via fft's, J. Comp. Phys., 57, 439-453.
12. Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F.G. (1954). Tables of Integral Transforms, Vol. 2 of Bateman Manuscript Project, McGraw-Hill, New York.
13. Flannery, B., Press, W., Teukolsky, S., and Vettering, W. (1992). Numerical Recipies in C, 2nd ed., Cambridge University Press, Cambridge, UK.
14. Hobson, E.W. (1931). The Theory of Spherical and Ellipsoidal Harmonics, Chelsea, New York.
15. Landau, L.D. and Lifschitz, E.M. (1977). Quantum Mechanics (Non-Relativistic Theory), 3rd ed., Pergamon Press, New York.
16. Matviyenko, G. (1996). Optimized local trigonometric bases, Appl. Comp. Harmon. Anal., 3(4), 301-323.
17. Mohlenkamp, M.J. (1997). A Fast Transform for Spherical Harmonics, Ph.D. Thesis, Yale University, New Haven, CT.
18. Orszag, S.A. (1986). Fast eigenfunction transforms, Advances in Mathematics Supplementary Studies, 10.
19. Stein, E. and Weiss, G. (1971). Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, NJ.
20. Szegö, G. (1975). Orthogonal Polynomials, 4th ed., AMS, Providence, RI.
21. Thiele, C.M. and Villemos, L.F. (1996). A fast algorithm for adapted time-frequency tilings, Appl. Comp. Harmon. Anal., 3(2), 91-99.
22. Wickerhauser, M.V. (1994). Adapted Wavelet Analysis from Theory to Software, Peters, A.K., Wellesley, MA.