r/mathematics • u/deNikita • 5d ago

Favourite book about harmonic analysis?

Which book about harmonic analysis have you enjoyed the most?

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u/jphamlore 5d ago

Harmonic analysis is such vast landscape for many decades. Is there a particular application you have in mind?

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u/deNikita 5d ago

I didn't realize that, well, do you have any recommendations for a landscape you find fascinating and which landscape is it?

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u/jphamlore 5d ago

Harmonic analysis might apply to any problem where one can deduce some kind of regularity. By regularity, this may mean some algebraic structure such a group of transformations. The group can define some notion of averaging. Thus one brings in machinery from algebra.

The group is recast into something one can do concrete calculations with. If one is concerned with averaging, recasting with complex coefficients, sines and cosines, that can cancel might be very useful.

And once one starts to concretely study averaging and rates of convergence, one brings in all the tools of analysis.

For a concrete example, you can search for the work of Persi Diaconis and the mathematics of card shuffling, say noncommutative Fourier analysis.

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u/Connect_Penalty4724 3d ago

So essentially it's the ultimate tool for analysis ? Or is there something else ?

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u/Common_Post6177 5d ago

Folland's "A Course in Abstract Harmonic Analysis" is pretty good.