A Volume Product Representation and Its Ramifications in lnp, 1≤p≤∞
Abstract: Let|Bnp|,1＜p＜∞ , be the volume of the unit p-ball in Rn and q the Hölder conjugate exponent of p. We represent the volume product |Bnp| |Bna| as a function free of its gamma symbolism. This representation will allows us in this particular case to confirm, using basic classical analysis tools, two conjectured and partially proved lower and upper bounds for the volume product of centrally symmetric convex bodies of the Euclidean Rn . These bounds in the general case play a central role in convex geometric analysis.
Keywords:
P-Ball,
Volume,
Gamma Function,
Infinite Product
Cite this paper:
nullD. Karayannakis, "A Volume Product Representation and Its Ramifications in lnp, 1≤p≤∞," Advances in Pure Mathematics, Vol. 1 No. 5, 2011, pp. 264-266. doi: 10.4236/apm.2011.15046.
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