Open Research Index

A proof of Kroó’s conjecture

Matthew J. Colbrook

Palomar Registrypalomar/PALOMAR-2026-10-27-000004Oct 27, 2026math.CAscore 0

For every origin-symmetric convex body with nonempty interior in a finite-dimensional real Euclidean space, continuous real boundary functions admit uniform approximation by real homogeneous polynomials of consecutive degrees. The development proves all thirteen principal results of the cited manuscript, including parity approximation, dimension-only uniform approximation of the constant function, homogeneous Gaussian kernels with polynomially weighted errors, fixed-bandwidth one-sided weighted density, tensor density, Gaussian Fourier cutoff, convex weighted approximation, finite-family…

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