Valuations on function spaces

DOI10.1515/ADVGEOM.2011.039zbMath1235.52023OpenAlexW2040955946MaRDI QIDQ3096814

Monika Ludwig

Publication date: 14 November 2011

Published in: advg (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/advgeom.2011.039

zbMATH Keywords

Sobolev spaceLebesgue spaceFisher information matrixvaluationLYZ operator

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Dissections and valuations (Hilbert's third problem, etc.) (52B45) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Ordered topological linear spaces, vector lattices (46A40)

Related Items (22)

Valuations on the Space of Quasi-Concave Functions ⋮ LYZ ellipsoid and Petty projection body for log-concave functions ⋮ Fourier transform and valuations ⋮ Translation invariant valuations on quasi-concave functions ⋮ The Hadamard variational formula and the Minkowski problem for \(p\)-capacity ⋮ Covariance matrices and valuations ⋮ Minkowski valuations on convex functions ⋮ General measure extensions of projection bodies ⋮ Hadwiger's theorem for definable functions ⋮ Volume, polar volume and Euler characteristic for convex functions ⋮ Minkowski additive operators under volume constraints ⋮ Starshaped sets ⋮ Dimension of the space of unitary equivariant translation invariant tensor valuations ⋮ Continuous valuations on the space of Lipschitz functions on the sphere ⋮ Invariant Valuations on Super-Coercive Convex Functions ⋮ \(\mathrm{SL}(n)\) covariant vector-valued valuations on \(L^p\)-spaces ⋮ \(\mathrm{SL}(m, \mathbb{C})\)-equivariant and translation covariant continuous tensor valuations ⋮ Hessian valuations ⋮ Monotone valuations on the space of convex functions ⋮ A class of invariant valuations on \(\operatorname{Lip}(S^{n -1})\) ⋮ Valuations on convex functions and convex sets and Monge-Ampère operators ⋮ \(L_p\)-Minkowski valuations on \(L^q\)-spaces

Cites Work

• Projection bodies in complex vector spaces
• Fisher information and matrix-valued valuations
• Invariant valuations on star-shaped sets
• Harmonic analysis of translation invariant valuations
• The concept of duality for measure projections of convex bodies
• Integral geometry of tensor valuations
• Crofton measures and Minkowski valuations
• A characterization of the duality mapping for convex bodies
• Affine Moser-Trudinger and Morrey-Sobolev inequalities
• The endomorphisms of the lattice of convex bodies
• The endomorphisms of the lattice of norms in finite dimensions
• Description of continuous isometry covariant valuations on convex sets
• Ellipsoids and matrix-valued valuations
• On the number of solutions to the discrete two-dimensional \(L_{0}\)-Minkowski problem.
• A new ellipsoid associated with convex bodies
• The discrete planar \(L_0\)-Minkowski problem
• The Cramer-Rao inequality for star bodies
• Projection bodies and valuations
• Moment-entropy inequalities.
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• Star valuations and dual mixed volumes
• Small ball probability estimates, \(\psi_2\)-behavior and the hyperplane conjecture
• Convex bodies and norms associated to convex measures
• The concept of duality in convex analysis, and the characterization of the Legendre transform
• Asymmetric affine \(L_p\) Sobolev inequalities
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• Normal and integral currents
• Geometry of log-concave functions and measures
• Blaschke valuations
• Intersection bodies and valuations
• Centroid Bodies and Dual Mixed Volumes
• Star body valued valuations
• Information theoretic inequalities
• Affine inequalities and radial mean bodies
• Minkowski valuations

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