On the average distance property and certain energy integrals

Arkiv for Matematik

Volumn 35, Issue 2, 1997, Pages 387-400

  Wolf, Reinhard ^a  

^a UNIVERSITY OF SALZBURG   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001221557     PISSN: 00042080     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02559976     Document Type: Article

References (19)

1. ALEXANDER, R. and STOLARSKY, K. B., Extremal problems of distance geometry related to energy integrals, Trans. Amer. Math. Soc. 193 (1974), 1-31.
2. BJÖRCK, G., Distributions of positive mass, which maximize a certain generalized energy integral, Ark. Mat. 3 (1958), 255-269.
3. CHOQUET, G., Lectures on Analysis, Vol. II: Representation Theory, Benjamin, New York-Amsterdam, 1969.
4. CLEARY, J., MORRIS, S. A. and YOST, D., Numerical geometry - numbers for shapes, Amer. Math. Monthly 93 (1986), 260-275.
5. 1, Israel J. Math. 24 (1976), 260-268.
6. GROSS, O., The rendezvous value of a metric space, in Advances in Game theory (Dresher, M., Shapley, L. S. and Tucker, A. W., eds.), Ann. of Math. Stud. 52, pp. 49-53, Princeton Univ. Press, Princeton, N. J., 1964.
7. HERZ, C., A class of negative definite functions, Proc. Amer. Math. Soc. 14 (1963), 670-676.
8. LÉVY, P., Théorie de l'addition des variables aléatoires, Gauthier-Villars, Paris, 1937.
9. LIN, P.-K., The average distance property of Banach spaces, Arch. Math. (Basel) 68 (1997), 496-502.
10. MORRIS, S. A. and NICKOLAS, P., On the average distance property of compact connected metric spaces, Arch. Math. (Basel) 40 (1983), 459-463.
11. NICHOLAS, P. and YOST, D., The average distance property for subsets of Euclidean space, Arch. Math. 50 (1988), 380-384.
12. PARTHASARATHY, K. R., Probability Measures on Metric Spaces, Academic Press, New York-London, 1967.
13. STOLARSKY, K. B., Sums of distances between points on a sphere, Proc. Amer. Math. Soc. 35 (1972), 547-549.
14. STOLARSKY, K. B., Sums of distances between points on a sphere, II, Proc. Amer. Math. Soc. 41 (1973), 575-582.
15. STRANTZEN, J., An average distance result in Euclidean n-space, Bull. Austral. Math. Soc. 26 (1982), 321-330.
16. WOLF, R., On the average distance property of spheres in Banach spaces, Arch. Math. 62 (1994), 378-384.
17. WOLF, R., On the average distance property in finite dimensional real Banach spaces, Bull. Austral. Math. Soc. 51 (1994), 87-101.
18. WOLF, R., Averaging distances in certain Banach spaces, Bull. Austral. Math. Soc. 55 (1997), 147-160.
19. YOST, D., Average distances in compact connected spaces, Bull. Austral. Math. Soc. 26 (1982), 331-342.