Literature cited
H. W. E. Jung, “Über die kleinste Kugel, die eine räumliche Figur einschliesst,” J. Reine Angew. Math.,123, 241–257 (1901).
H. F. Bohnenblust, “Convex regions and projections in Minkowski spaces,” Ann. Math.,39, No. 2, 301–308 (1938).
L. Danzer, B. Grunbaum, and V. Klee, Helly's Theorem [Russian translation], Mir, Moscow (1968).
D. M. Burago and V. A. Zalgaller, Geometric Inequalities [in Russian], Nauka, Leningrad (1980).
N. A. Routledge, “A result in Hilbert space,” Q. J. Math.,3, 12–18 (1952).
V. I. Berdyshev, “The connection between Jackson's inequality and a certain geometrical problem,” Mat. Zametki,3, No. 3, 327–338 (1968).
V. I. Berdyshev, “Jackson's theorem in Lp,” Tr. Mat. Inst. Akad. Nauk SSSR,88, 3–16 (1967).
N. I. Chernykh, “Jackson's inequality in Lp,” Tr. Mat. Inst. Akad. Nauk SSSR,88, 71–74 (1967).
A. D. Ioffe and V. M. Tikhomirov, Theory of Extremal Problems [in Russian], Nauka, Moscow (1974).
M. N. Arshinov and L. E. Sadovskii, Codes and Mathematics [in Russian], Nauka, Moscow (1983).
J. Wells and L. Williams, Embeddings and Extensions in Analysis, Springer, Heidelberg (1975).
V. L. Dol'nikov, “Jung's constant in l1 n,” Mat. Zametki,42, No. 4, 519–526 (1987).
I. M. Vinogradov, Elements of Number Theory [in Russian], Nauka, Moscow (1981).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 43, No. 5, pp. 604–614, May, 1988.
The author thanks V. A. Yudin for helpful conversations. Chernykh's investigation on Jackson's theorem in Lp had great significance for the author.
Rights and permissions
About this article
Cite this article
Pichugov, S.A. Jung's constant for the space Lp . Mathematical Notes of the Academy of Sciences of the USSR 43, 348–354 (1988). https://doi.org/10.1007/BF01158839
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01158839