A functional analytic approach to intersection bodies

By Alexander Koldobsky. 2000

101 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/96909c56af8fa2fad78c93eb7bed39f7c66efb68

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In Applied Mathematics

Citations in the corpus

The Busemann-Petty problem for arbitrary measures (2004, methodology): “Corollary 3 is a generalization of a result of Koldobsky ([ K7 ], Theorem 8; see also [RZ]), where the case of n k = 3 and M = Bn 2 was considered.”
Convolutions and multiplier transformations of convex bodies (2007, background): “Intersection bodies turned out to be critical for the solution of the Busemann-Petty problem, see [8], [9], [11], [19], [21], [22], [56].”
Generalized intersection bodies (2005, methodology): “in [BZ98] (see also a correction in [RZ04]), and later in [ Kol00 ], that the answer is negative for k Kol00 ], is that of a k-intersection body.”
Volume inequalities and additive maps of convex bodies (2006, background): “Intersection bodies turned out to be critical for the solution of the Busemann-Petty problem, see [6], [7], [9], [14], [16], [17], [40].”
A characterization of Lp intersection bodies (2006, background): “For a hyperplane H ⊂ Rn, Pn0 (H) is the set of convex polytopes in H containing the origin in their interiors relative to H.”
Dual mixed volumes and the slicing problem (2005, background): “Theorem 2 should be understood as a partial complimentary result to Theorem 1. The reason for this may be better explained, if we first consider a second generalization of intersection bodies, introduced by Koldobsky in [ Kol00 ].”
Valuations and Busemann{Petty Type Problems (2008, background): “Although the notion of intersection bodies is relatively new, the topic has been intensively studied in recent years, see [17,20,27,34,40,51] and the books [13,35,65].”
Intersection bodies and Lp-spaces (2005, methodology): “general connection between intersection bodies and embedding in Lp established in [ Ko3 ]:”