Reconstruction of a polynomial from its radon projections

SIAM Journal on Mathematical Analysis

Volumn 37, Issue 1, 2005, Pages 238-250

  Bojanov, Borislav ^a   Xu, Yuan ^b  

^a UNIVERSITY OF SOFIA   (Bulgaria)

^b UNIVERSITY OF OREGON   (United States)

Author keywords

Interpolation; Polynomials of two variables; Radon projection

Indexed keywords

POLYNOMIALS OF TWO VARIABLES; RADON PROJECTION;

INTERPOLATION; RADON;

POLYNOMIALS;

EID: 33144475230     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/040616516     Document Type: Article

References (19)

1. B. BOJANOV AND I. K. GEORGIEVA, Interpolation by bivariate polynomials based on Radon projections, Studia Math., 162 (2004), pp. 141-160.
2. B. BOJANOV AND Y. Xu, On a Hermite interpolation by polynomials of two variables, SIAM J, Numer. Anal., 39 (2002), pp. 1780-1793.
3. B. BOJANOV AND Y. Xu, On polynomial interpolation of two variables, J. Approx. Theory, 120 (2003), pp. 267-282.
4. A. S. CAVARETTA, C. A. MICCHELLI, AND A. SHARMA, Multivariate interpolation and the Radon transform, Part I, Math. Z., 174 (1980), pp. 263-279.
5. A. S. CAVARETTA, C. A. MICCHELLI, AND A. SHARMA, Multivariate interpolation. II. Some further examples, in Quantitive Approximation, R. A. DeVore and K. Scherer, eds., Acad. Press, New York, London, 1980, pp. 49-62.
6. C. F. DUNKL AND Y. Xu, Orthogonal Polynomials of Several Variables, Cambridge University Press, Cambridge, UK, 2001.
7. H. HAKOPIAN, Multivariate divided differences and multivariate interpolation of Lagrange and Hermite type, J. Approx. Theory, 34 (1982), pp. 286-305.
8. H. HAKOPIAN, Multivariate spline functions, B-spline basis and polynomial interpolation II, Studia Math., 79 (1984), pp. 91-102.
9. H. HAKOPIAN AND S. ISMAEIL, On a bivariate interpolation problem, J. Approx. Theory, 116 (2002), pp. 76-99.
10. C. HAMAKER AND D. C. SOLMON, The angles between the null spaces of X-rays, J. Math. Anal. Appl., 62 (1978), pp. 1-23.
11. B. LOGAN AND L. SHEPP, Optimal reconstruction of a function from its projections, Duke Math. J., 42 (1975), pp. 645-659.
12. R. MARR, On the reconstruction of a function on a circular domain from a sampling of its line integrals, J. Math. Anal. Appl., 45 (1974), pp. 357-374.
13. P. NATTERER, The Mathematics of Computerized Tomography, Classics in Appl. Math. 32, SIAM, Philadelphia, 2001.
14. N. OBRECHKOFF, Zeros of Polynomials, Bulgarian Academic Monographs 7, Marin Drinov Academic Publishing House, Sofia, 2003.
15. T. J. RIVLIN, Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory, 2nd ed., Wiley, New York, 1990.
16. D. C. SOLMON, The X-ray transform, J. Math. Anal. Appl., 56 (1976), pp. 61-83.
17. Y. Xu, Funk-Hecke formula for orthogonal polynomials on spheres and on balls, Bull. London Math. Soc., 32 (2000), pp. 447-457.
18. Y. Xu, Polynomial interpolation on the unit sphere, SIAM J. Numer. Anal., 41 (2003), pp. 751-766.
19. A. ZYGMUND, Trigonometric Series, Cambridge University Press, Cambridge, UK, 1959.