Lower bounds for spherical designs

Canadian Plastics Magazine

Volumn 61, Issue 3, 1997, Pages 673-683

  Yudin, V A ^a  

^a NONE

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EID: 33748089374     PISSN: 00084778     EISSN: None     Source Type: Trade Journal    
DOI: None     Document Type: Article

References (15)

1. J. Conway and N. J. A. Sloane, Sphere packings, lattices, and groups, Springer-Verlag Berlin-New York 1988; Russian transi., Mir, Moscow 1990.
2. B. Resnick, "Sums of even powers of real linear forms", Mem. American Math. Soc. 96 no. 463 (1992).
3. J. Seidel, "Isometric embeddings and geometric designs", Discrete Math. 136 (1994), 281 293.
4. V. M. Sidel'nikov, "On extremal polynomials used in bounds of the cardinality of a code" Problemy Peredachi Informatsii 14:3 (1980), 17-30; English transi, in Problems Inform Transmission 14 (1980).
5. V. I. Levenshtein, "On bounds for packings in n-dimensional Euclidean space", Dokl. Akad Nauk SSSR 245 (1979), 1299-1303; English transi, in Soviet Math. Dokl. 20 (1979).
6. V. I. Levenshtein, "Bounds for packings of metric spaces and some of their applications" Problemy Kibemet. 40 (1983), 43-110. (Russian)
7. N. I. Chernykh, "On best approximation of periodic functions by trigonometric polynomial in L2", Mat. Zametki 2 (1967), 513-522; English transi, in Math. Notes 2 (1967).
8. V. A. Yudin, The multidimensional Jackson theorem in I/a", Mat. Zametki"29 (1981) 309-315; English transi, in Math. Notes 29 (1981).
9. P. Delsarte, J. M. Goethals, and J. J. Seidel, "Spherical codes and design", Geom. Dedicat 6 (1977), 363-388.
10. P. Boyvalenkov, "Extremal Polynomials for obtaining Bounds for Spherical Codes an Designs", Discrete Comput. Geom. 14 (1995), 167-183.
11. G. Szegö, Orthogonal polynomials, rev. ed., American Math. Soc., Providence, RI 1959 Russian transi., with an appendix by Ya. L. Geronimus, Fizmatgiz, Moscow 1961; Englis transi, of appendix, American Math. Soc. Transi. (2), Vol. 108, American Math. Soc. Providence, RI 1977, pp. 37-130.
12. R. Courant and D. Hilbert, Methoden der mathematischen Physik Vol. I, 2nd ed. Springer-Verlag, Berlin 1931; English transi., Interscience, New York 195.3; Russian transi. Gostekhizdat, Moscow 1951.
13. S. L. Sobolev, Introduction to the theory of cubature formulae, Nauka, Moscow 1974 (Russian)
14. R. H. Hardin and N. J. A. Sloane, "New spherical 4-designs", Discrete Math. 106/107 (1992), 255-264.
15. E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeto Univ. Press, Princeton, NJ 1971; Russian transi., Mir, Moscow 1974. Moscow Institute of Energy