I'm trying to find a good reference for harmonic analysis. I'm not talking yet about abstract one on locally compact groups, but rather regular fourier on the real line.

My problem is that all books I've looked at assume that the reader has only learned about riemann integral and in general seem to assume little mathmatical maturity.

Can anyone recommand a reference to someone who is comfortable with measure theory for harmonic analysis- in particular I want the general statements to work with Lebesgue measure, define fourier transform on a large as possible set of functions.

Maybe I should be jumping straight to fourier on locally compact and the abstract type?



Two sources I found useful.

I disdained books, so I did not search well among them.




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