The Fourier transform on valuations is the Fourier transform

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Integral geometry (53C65) Other transforms and operators of Fourier type (43A32) Dissections and valuations (Hilbert's third problem, etc.) (52B45)

Cites Work

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Classification of invariant valuations on the quaternionic plane
Integral geometry and valuations. Notes of the lectures given in the advanced course on integral geometry and valuation theory, Barcelona, Spain, September 6--10, 2010. Edited by Eduardo Gallego and Gil Solanes
A Fourier-type transform on translation-invariant valuations on convex sets
Valuations on manifolds and integral geometry
Hermitian integral geometry
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The Weyl principle on the Finsler frontier
Valuations on manifolds and Rumin cohomology
Valuations with Crofton formula and Finsler geometry
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Continuous translation invariant valuations on the space of compact convex sets
An analytic solution to the Busemann-Petty problem on sections of convex bodies
Integral geometry in Minkowski spaces
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Some relations between curvature and characteristic classes
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A Fourier analytic proof of the Blaschke-Santaló Inequality
Distributions and Valuations
Cube Slicing in R n
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The Hörmander Proof of the Bourgain–Milman Theorem
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Classical Fourier Analysis
Algebraic Integral Geometry
Convex and Discrete Geometry
Kinematic formulas on the quaternionic plane
Convex Bodies The Brunn-MinkowskiTheory
Fourier integral operators
Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture

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