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Banach limit in convexity and geometric means for convex bodies
1. | University of Minnesota, School of Mathematics, United States |
References:
[1] |
S. Artstein-Avidan and V. Milman, The concept of duality for measure projections of convex bodies, J. Funct. Anal., 254 (2008), 2648-2666.
doi: 10.1016/j.jfa.2007.11.008. |
[2] |
K. J. Böröczky and R. Schneider, A characterization of the duality mapping for convex bodies, Geom. Funct. Anal., 18 (2008), 657-667.
doi: 10.1007/s00039-008-0676-5. |
[3] |
P. M. Gruber, The endomorphisms of the lattice of norms in finite dimensions, Abh. Math. Sem. Univ. Hamburg, 62 (1992), 179-189.
doi: 10.1007/BF02941625. |
[4] |
J. Lawson and Y. Lim, The geometric mean, matrices, metrics, and more, Amer. Math. Monthly, 108 (2001), 797-812.
doi: 10.2307/2695553. |
[5] |
P. D. Lax, Functional Analysis, Pure and Applied Mathematics (New York), Wiley-Interscience [John Wiley & Sons], New York, 2002. |
[6] |
V. Milman and L. Rotem, Non-standard constructions in convex geometry; geometric means of convex bodies,, in Convexity, ().
|
[7] |
I. Molchanov, Continued fractions built from convex sets and convex functions, Commun. Contemp. Math., 17 (2015), 1550003, 18 pp.
doi: 10.1142/S0219199715500030. |
[8] |
L. Rotem, Algebraically inspired results on convex functions and bodies, Commun. Contemp. Math., 18 (2016), 1650027, 14 pp.
doi: 10.1142/S0219199716500279. |
[9] |
R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Second expanded edition, Encyclopedia of Mathematics and its Applications, 151, Cambridge University Press, Cambridge, 2014. |
show all references
References:
[1] |
S. Artstein-Avidan and V. Milman, The concept of duality for measure projections of convex bodies, J. Funct. Anal., 254 (2008), 2648-2666.
doi: 10.1016/j.jfa.2007.11.008. |
[2] |
K. J. Böröczky and R. Schneider, A characterization of the duality mapping for convex bodies, Geom. Funct. Anal., 18 (2008), 657-667.
doi: 10.1007/s00039-008-0676-5. |
[3] |
P. M. Gruber, The endomorphisms of the lattice of norms in finite dimensions, Abh. Math. Sem. Univ. Hamburg, 62 (1992), 179-189.
doi: 10.1007/BF02941625. |
[4] |
J. Lawson and Y. Lim, The geometric mean, matrices, metrics, and more, Amer. Math. Monthly, 108 (2001), 797-812.
doi: 10.2307/2695553. |
[5] |
P. D. Lax, Functional Analysis, Pure and Applied Mathematics (New York), Wiley-Interscience [John Wiley & Sons], New York, 2002. |
[6] |
V. Milman and L. Rotem, Non-standard constructions in convex geometry; geometric means of convex bodies,, in Convexity, ().
|
[7] |
I. Molchanov, Continued fractions built from convex sets and convex functions, Commun. Contemp. Math., 17 (2015), 1550003, 18 pp.
doi: 10.1142/S0219199715500030. |
[8] |
L. Rotem, Algebraically inspired results on convex functions and bodies, Commun. Contemp. Math., 18 (2016), 1650027, 14 pp.
doi: 10.1142/S0219199716500279. |
[9] |
R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Second expanded edition, Encyclopedia of Mathematics and its Applications, 151, Cambridge University Press, Cambridge, 2014. |
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