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  "body": "\n## Summary\n\nThe Jackson kernel is a nonnegative trigonometric polynomial, the normalised square of the [[Fejér kernel|DCCA2T9GKH]].\nConvolution with it gives trigonometric polynomials that approximate a continuous periodic function with error of order $\\omega(f, 1/n)$.\nIt is the standard tool in the proof of Jackson's inequality.\n\n## Explanations\n\n### L1 human\n\nAveraging a function against a narrow bump smooths it and keeps it close to the original.\nIf the bump is itself a trigonometric polynomial, the average is a trigonometric polynomial too.\nThe Fejér kernel is such a bump, but its tails are too heavy for the best error bounds.\nSquaring it makes the tails much thinner, which is exactly what Jackson's proof needs.\n",
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