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1995 | 34 | 1 | 79-87
Tytuł artykułu

Isometric imbeddings of Euclidean spaces into finite dimensional $l_p$-spaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is shown that $l^n_2$ imbeds isometrically into $l^{n^2+1}_4$ provided that n is a prime power plus one, in the complex case. This and similar imbeddings are constructed using elementary techniques from number theory, combinatorics and coding theory. The imbeddings are related to existence of certain cubature formulas in numerical analysis.
Słowa kluczowe
Rocznik
Tom
34
Numer
1
Strony
79-87
Opis fizyczny
Daty
wydano
1995
Twórcy
  • Mathematisches Seminar, Universität Kiel, Ludewig-Meyn-Str. 4, 24098 KIEL, Germany
Bibliografia
  • [B] E. Bannai, On extremal finite sets in the sphere and other metric spaces, London Math. Soc. Lecture Notes Ser. 131 (1986), 13-38.
  • [DGS] P. Delsarte, J. M. Goethals, J. J. Seidel, Spherical codes and designs, Geom. Dedicata 6 (1977), 363-388.
  • [FLM] T. Figiel, J. Lindenstrauss, V. Milman, The dimension of almost spherical sections of convex bodies, Acta Math. 139 (1977), 53-94.
  • [GS] J. M. Goethals, J. J. Seidel, Cubature formulae, polytopes and spherical designs, in: The geometric vein, Coxeter Festschrift, ed. C. Davis et al. Springer 1981, 203-218.
  • [Ho] S. G. Hoggar, t-designs in projective spaces, European J. Combin. 3 (1982), 233-254.
  • [HR] H. Halberstam, K. Roth, Sequences, Springer 1983.
  • [Hu] Hua Loo Keng, Introduction to number theory, Springer 1982.
  • [KT] H. König, N. Tomczak-Jaegermann, Norms of minimal projections, J. Funct. Anal. 119 (1994), 253-280.
  • [L] Yu. Lyubich, On the boundary spectrum of a contraction in Minkovsky spaces, Siberian Math. J. 11 (1970), 271-279.
  • [LV] Yu. Lyubich, L. Vaserstein, Isometric imbeddings between classical Banach spaces, cubature formulas, and spherical designs, Geom. Dedicata 47 (1993), 327-362.
  • [M] V. Milman, A few observations on the connections between local theory and some other fields, in: Geometric aspects of functional analysis, Lecture Notes in Math. 1317 (1988), 283-289.
  • [MS] F. Mac Williams, N. Sloane, The theory of error-correcting codes II, North Holland 1977.
  • [R] B. Reznick, Sums of even powers of real linear forms, Mem. Amer. Math. Soc. 96 (1992), no. 463.
  • [S] J. J. Seidel, Isometric embeddings and geometric designs, preprint Eindhoven 1993, to appear in Trends in Discrete Mathematics.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv34i1p79bwm
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