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Sorry for such a newbie post and for asking two unrelated references in one shot. First, I am interested in any proof of Pinsker's inequality. Second, I wonder what is the best place to read about Pontryagin duality and harmonic analysis. To clarify, I took only standard functional analysis course. |
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Folland's book ("A Course in Abstract Harmonic Analysis") is highly extensive, developing the machinery of spectral theory, Banach algebras, topological groups and the unitary representation theory of arbitrary LCH groups before arriving at the more specific theory of (locally compact Hausdorff) abelian groups. Later he also gives very general treatments of the theory of compact groups and of the construction of induced representations, and finally, he lays down the general results known for arbitrary LCSC (locally compact, second countable and Hausdorff) groups in harmonic analysis, mostly without proof. In my opinion this book is great but it is probably too heavy for you if you're just interested in the abelian theory. In that case Katznelson's "An Introduction to Harmonic Analysis" is a nice book which may be more suitable for you. |
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I found Rudin's "Fourier Analysis on Groups" a good reference for Pontryagin duality. The level of functional analysis there is not too high. |
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proof of pinkser's inequality: http://www.clsp.jhu.edu/~sanjeev/520.674/notes/I-divergence-properties.pdf |
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