\(L_p\)-Minkowski valuations on \(L^q\)-spaces

DOI10.1016/j.jmaa.2013.12.048zbMath1331.52022OpenAlexW249404267MaRDI QIDQ2338728

Michael Ober

Publication date: 27 March 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2013.12.048

zbMATH Keywords

convex bodycharacterization theorem\(L_p\)-Brunn-Minkowski theory\(\mathrm{SL}(n)\)-covariance\(L_p\)-Minkowski sum\(L_p\)-Minkowski valuation\(L_p\)-moment operator\(p\)-th moment measure

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Dissections and valuations (Hilbert's third problem, etc.) (52B45) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (16)

Valuations on the Space of Quasi-Concave Functions ⋮ Real-valued valuations on Sobolev spaces ⋮ Fourier transform and valuations ⋮ \(L_{p}\) Minkowski valuations on polytopes ⋮ Laplace transforms and valuations ⋮ Translation invariant valuations on quasi-concave functions ⋮ Geometric valuation theory ⋮ Minkowski valuations on convex functions ⋮ Volume, polar volume and Euler characteristic for convex functions ⋮ Invariant Valuations on Super-Coercive Convex Functions ⋮ \(\mathrm{SL}(n)\) covariant vector-valued valuations on \(L^p\)-spaces ⋮ Hessian valuations ⋮ Monotone valuations on the space of convex functions ⋮ Valuations on log-concave functions ⋮ A class of invariant valuations on \(\operatorname{Lip}(S^{n -1})\) ⋮ The support of dually epi-translation invariant valuations on convex functions

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