Artículo

Carando, D.; Galicer, D.; Pinasco, D. "Energy integrals and metric embedding theory" (2015) International Mathematics Research Notices. 2015(16):7417-7435
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Abstract:

For some centrally symmetric convex bodies K CRn, we study the energy integral where the supremum runs over all finite signed Borel measures μ on K of total mass one. In the case where K = Bn q, the unit ball of Bnq (for 1<q ≤ 2) or an ellipsoid, we obtain the exact value or the correct asymptotical behavior of the supremum of these integrals. We apply these results to a classical embedding problem in metric geometry. We consider in Rn the Euclidean distance d2. For 0<α<1, we estimate the minimum R for which the snowflaked metric space (K,dα2) may be isometrically embedded on the surface of a Hilbert sphere of radius R. © 2014 The Author(s).

Registro:

Documento: Artículo
Título:Energy integrals and metric embedding theory
Autor:Carando, D.; Galicer, D.; Pinasco, D.
Filiación:Departamento de Matematica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pab. i, Cdad Universitaria (C1428EGA), Buenos Aires, Argentina
IMAS-CONICET, Argentina
Departamento de Matematicas y Estadstica, Universidad T. di Tella, Av. Figueroa Alcorta 7350, Buenos Aires, C1428BCW, Argentina
CONICET, Argentina
Año:2015
Volumen:2015
Número:16
Página de inicio:7417
Página de fin:7435
DOI: http://dx.doi.org/10.1093/imrn/rnu169
Título revista:International Mathematics Research Notices
Título revista abreviado:Int. Math. Res. Not.
ISSN:10737928
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10737928_v2015_n16_p7417_Carando

Referencias:

  • Albiac, F., Kalton, N.J., Topics in Banach space theory (2006) Graduate Texts in Mathematics, 233. , New York: Springer
  • Alexander, R., Two notes on metric geometry (1977) Proceedings of the American Mathematical Society, 64 (2), pp. 317-320
  • Alexander, R., Geometric methods in the study of irregularities of distribution (1990) Combinatorica, 10 (2), pp. 115-136
  • Alexander, R., Principles of a new method in the study of irregularities of distribution (1991) Inventiones Mathematicae, 103 (1), pp. 279-296
  • Alexander, R., Stolarsky, K.B., Extremal problems of distance geometry (1974) Transactions of the American Mathematical Society, 193, pp. 1-31
  • Assouad, P., Plongements lipschitziens dans Rn (1983) Bulletin de la Société Mathématique de France, 111 (4), pp. 429-448
  • Baumbach, G., Linde, W., Asymptotic behaviour of p-absolutely summing norms of identity operators (1977) Mathematische Nachrichten, 78 (1), pp. 193-196
  • Björck, G., Distributions of positive mass which maximize a certain generalized energy integral (1956) Arkiv för Matematik, 3 (3), pp. 255-269
  • Defant, A., Floret, K., Tensor norms and operator ideals (1993) North-Holland Mathematics Studies, 176. , Amsterdam: North-Holland xi, 566 pp
  • Diestel, J., Jarchow, H., Tonge, A., Absolutely summing operators (1995) Cambridge Studies in Advanced Mathematics, 43. , Cambridge: Cambridge University Press
  • Fejes Tóth, L., On the sum of distances determined by a pointset (1956) Acta Mathematica Academiae Scientiarum Hungaricae, 7 (3-4), pp. 397-401
  • Hinrichs, A., Nickolas, P., Wolf, R., A note on the metric geometry of the unit ball (2011) Mathematische Zeitschrift, 268 (3-4), pp. 887-896
  • Kelly, J.B., Combinatorial inequalities (1970) Combinatorial Structures and Their Applications, pp. 201-207. , edited by R. Guy, H. Hanani, N. Sauer, and J. Schonheim New York: Gordon and Breach
  • Naor, A., Neiman, O., Assouad's theorem with dimension independent of the snowflaking (2012) Revista Matemtica Iberoamericana, 28 (4), pp. 1123-1142
  • Nickolas, P., Wolf, R., Distance geometry in quasihypermetric spaces. i (2009) Bulletin of the Australian Mathematical Society, 80 (1), pp. 1-25
  • Nickolas, P., Wolf, R., Distance geometry in quasihypermetric spaces. II (2011) Mathematische Nachrichten, 284 (2-3), pp. 332-341
  • Nickolas, P., Wolf, R., Distance geometry in quasihypermetric spaces. III (2011) Mathematische Nachrichten, 284 (5-6), pp. 747-760
  • Nielson, F., Om summen af afstandene mellem n punkter pa en Kugleflade (1965) Nordisk Matematisk Tidskrift, 13, pp. 45-50
  • Pietsch, A., (1978) Operator Ideals. Mathematische Monographien [Mathematical Monographs], 16. , Berlin: VEB Deutscher Verlag der Wissenschaften
  • Pólya, G., Szegö, G., Ü ber den transfiniten Durchmesser (Kapazitätskonstante) von ebe-nen und räumlichen Punktmengen (1931) Journal für Die Reine und Angewandte Mathematik, 165, pp. 4-49
  • Rogers, A.D., A functional from geometry with applications to discrepancy estimates and the Radon transform (1994) Transactions of the American Mathematical Society, 341 (1), pp. 275-313
  • Schoenberg, I., On certain metric spaces arising from Euclidean spaces by a change of metric and their imbedding in Hilbert space (1937) Annals of Mathematics, 38 (4), pp. 787-793
  • Schoenberg, I., Von-Neumann, J., Fourier integrals and metric geometry (1941) Transactions of the American Mathematical Society, 50 (2), pp. 226-251
  • Schur, I., Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten (1918) Mathematische Zeitschrift, 1 (4), pp. 377-402
  • Sperling, G., Losung einer elementargeometrischen Frage von Fej56 Toth (1960) Archiv der Mathematik, 11 (1), pp. 69-71
  • Spira, R., Calculation of the gamma function by Stirling's formula (1971) Mathematics of Computation, 25 (114), pp. 317-322
  • Tomczak-Jaegermann, N., Banach-Mazur distances and finite-dimensional operator ideals (1989) Pitman Monographs and Surveys in Pure and Applied Mathematics, 38. , Harlow: Longman Scientific &amp; Technical; New York: John Wiley & Sons, Inc. xii, 395 pp
  • Wilson, W.A., On certain types of continuous transformations of metric spaces (1935) American Journal of Mathematics, 57 (1), pp. 62-68

Citas:

---------- APA ----------
Carando, D., Galicer, D. & Pinasco, D. (2015) . Energy integrals and metric embedding theory. International Mathematics Research Notices, 2015(16), 7417-7435.
http://dx.doi.org/10.1093/imrn/rnu169
---------- CHICAGO ----------
Carando, D., Galicer, D., Pinasco, D. "Energy integrals and metric embedding theory" . International Mathematics Research Notices 2015, no. 16 (2015) : 7417-7435.
http://dx.doi.org/10.1093/imrn/rnu169
---------- MLA ----------
Carando, D., Galicer, D., Pinasco, D. "Energy integrals and metric embedding theory" . International Mathematics Research Notices, vol. 2015, no. 16, 2015, pp. 7417-7435.
http://dx.doi.org/10.1093/imrn/rnu169
---------- VANCOUVER ----------
Carando, D., Galicer, D., Pinasco, D. Energy integrals and metric embedding theory. Int. Math. Res. Not. 2015;2015(16):7417-7435.
http://dx.doi.org/10.1093/imrn/rnu169