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Feb 17 at 6:15 vote accept Antonius
Feb 16 at 21:02 comment added Christian Remling @IosifPinelis: Not sure, but it's certainly possible. Maybe one can just take one of the constructions of a continuous (and periodic) function with divergent Fourier series, and $f-c$ might still work in the current setting.
Feb 16 at 20:52 history edited Iosif Pinelis CC BY-SA 4.0
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Feb 16 at 20:51 comment added Iosif Pinelis Nice use of the uniform boundedness principle. Do you think an explicit example can be constructed here?
Feb 16 at 20:23 history answered Christian Remling CC BY-SA 4.0