Spherical harmonics in texture analysis

Tectonophysics

Volumn 370, Issue 1-4, 2003, Pages 253-268

  Schaeben, Helmut ^a   van den Boogaart, K Gerald ^a  

^a TU BERGAKADEMIE FREIBERG   (Germany)

Author keywords

Harmonic series expansions; Methods of texture analysis; Real valued harmonics for the rotation group; Real valued spherical harmonics; Spectral decomposition of the X ray transform; Spherical radial basis functions; Spherical singular integral; Spherical wavelets; Summability

Indexed keywords

MATHEMATICS; PREFERRED ORIENTATION; ROTATION; SPHERE; SPHERICAL HARMONICS; TEXTURE; WAVELET;

EID: 0042973792     PISSN: 00401951     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0040-1951(03)00190-2     Document Type: Article

References (38)

1. Arnold, K.J., 1941. On spherical probability distributions. PhD thesis, Massachusetts Institute of Technology, MA, USA.
2. Berens H. Butzer P.L. Pawelke S. Limitierungsverfahren von Reihen mehrdimensionaler Kugelfunktionen und deren Saturationsverhalten Publ. Res. Inst. Math. Sci., Kyoto Univ., Ser. A 4 1968 201-268
3. Boogaart, K.G.V.D., 2001. Statistics for individual crystallographic orientation measurements. PhD Thesis, Freiberg.
4. Boogaart K.G.v.d. Schaeben H. Singular value decomposition of the odf-pdf projection operator Szpunar J.A. Proceedings of the 12th International Conference on Textures of Materials (ICOTOM12) 1999 1363-1368 NRC Research Press Ottawa, Ont., Canada
5. Bunge H.J. Mathematische Methoden der Texturanalyse 1969 Akademie Verlag Berlin
6. Bunge H.J. Texture Analysis in Materials Science 1982 Butterworths London
7. Butzer P.L. Nessel R.J. Fourier Analysis and Approximation 1971 Birkhäuser Verlag Basel
8. Butzer P.L. Stens R.L. Wehrens H. Approximation by algebraic convolution integrals Prolla J.B. Approximation Theory and Functional Analysis 1979 71-120 North Holland Publishing Amsterdam
9. Cerejeiras P. Schaeben H. Sommen F. The spherical X-ray transform Math. Methods Appl. Sci. 25 2002 1493-1507
10. Curtis C.W. Reiner J. Representation Theory of Finite Groups and Associative Algebras 1962 Interscience New York
11. Dunkl C.F. Operators and harmonic analysis on the sphere Trans. Am. Math. Soc. 125 1966 250-263
12. Eschner T. Texture analysis by means of model functions Textures Microstruct. 21 1993 139-146
13. Eschner T. Generalized model function for quantitative texture analysis Bunge H.J. Siegesmund S. Skrotzki W. Weber K. Textures of Geological Materials 1994 15-28 DGM Informationsgesellschaft Oberursel
14. Freeden W. Gervens T. Schreiner M. Constructive Approximation on the Sphere with Applications to Geomathematics 1998 Clarendon Press Oxford
15. Funk P. Über Flächen mit lauter geschlossenen geodätischen Linien Math. Ann. 74 1913 278-300
16. Funk P. ÜUber eine geometrische Anwendung der Abel'schen Integralgleichung Math. Ann. 77 1916 129-135
17. Gel'fand I.M. Minlos R.A. Shapiro Z.Ya. Representations of the Rotation and Lorentz Groups and Their Applications 1963 Pergamon Oxford
18. Hochstadt H. The Functions of Mathematical Physics 1986 Wiley New York
19. Ivanova T.M. Nikolayev D.I. New standard function for quantitative texture analysis Phys. Stat. Solidi, B 228 2001 825-836
20. Mardia K.V. Jupp P.E. Directional Statistics 2000 Wiley New York
21. Matthies S. Standard functions in texture analysis Phys. Stat. Solidi, B 101 1980 K111-K115
22. Matthies S. Vinel G.W. Helming K. Standard Distributions in Texture Analysis vol. I 1987 Akademie Verlag Berlin
23. Matthies S. Helming K. Steinkopf T. Kunze K. Standard distributions for the case of fibre textures Phys. Stat. Solidi, B 150 1988 K1-K5
24. Matthies S. Vinel G.W. Helming K. Standard Distributions in Texture Analysis vol. III 1990 Akademie Verlag Berlin
25. Mhaskar H.N. Narcowich F.J. Prestin J. Ward J.D. Polynomial frames on the sphere Adv. Comput. Math. 2001 (in press)
26. Nikolayev D.I. Savyolova T.I. Normal distribution on the rotation group SO(3) Textures Microstruct. 29 1997 201-233
27. Potts D. Steidl G. Tasche M. Kernels of spherical harmonics and spherical frames Fontanella F. Jetter K. Laurent P.-J. Advanced Topics in Multivariate Approximation 1996 287-301 World Scientific Publications Singapore
28. Radon J. Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig Math.-Phys. Klasse 69 1917 262-277
29. Savelova, T.I. [identical with Savyolova], 1984. Distribution functions of grains with respect to orientation in polycrystals and their Gaussian approximations. Ind. Lab. 50, 468-474 (translated from Zavod. Lab. 50, 48, 52).
30. 4 J. Appl. Crystallogr. 29 1996 516-525
31. Schaeben H. A unified view of methods to resolve the inverse problem of texture goniometry Textures Microstruct. 25 1996b 171-181
32. Schaeben H. A simple standard orientation density function: The hyperspherical de la Vallëe Poussin kernel Phys. Stat. Solidi, B 200 1997 367-376
33. Schaeben H. The de la Vallée Poussin standard orientation density function Proceedings of the International Conference on Neutron Texture and Stress Analysis, Dubna, Russia, June 23-26, 1997 Textures Microstruct. 33 1999 365-373 (Special Issue)
34. Schaeben H. Nikolayev D.I. The central limit theorem in texture component fit methods Acta Appl. Math. 53 1998 59-87
35. Schaeben H. Potts D. Prestin J. Spherical wavelets with an application in preferred crystallographic orientation Proceedings of the Annual Conference of the International Association for Mathematical Geology, Cancun, Mexico, Sep 6-12, 2001 2001
36. Vilenkin, N.J., 1968. Special Functions and the Theory of Group Representations. Am. Math. Soc. Transl. of Math. Monographs 22, Providence, 613 pp.
37. Watson G.S. Statistics on Spheres 1983 Wiley New York
38. Zheng Y. Doerschuk P.C. Explicit computation of orthonormal symmetrized harmonics with applications to the identity representation of the icosahedral group SIAM J. Math. Anal. 32 3 2000 538-554