Stein's Singular Integrals book mentions a number of results concerned with characterising operators that commute with translations. Some of those results are mentioned in this other StackExchange post. Are there any examples of questions/problems where one can see the need for such operators? How would one motivate the problem of characterising such operators (for someone with an understanding of analysis at the level of Folland/Royden)?
2026-04-03 18:41:18.1775241678
Why are linear operators that commute with translation important?
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