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What texts/books are available for progressing into non-commutative harmonic analysis?

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"Soft questions" (question that don't really have an answer) should generally be made "community wiki". I've converted this one to wiki, but in the future you should check the "community wiki" box in the lower right hand corner of the input field. Of course, specific questions that "have answers" should usually not be community wiki. – Anton Geraschenko Nov 6 '09 at 17:48

I especially like

Lang: SL(2,R) (There is more than just SL(2,R) there)

Folland: A course in abstract harmonic analysis (especially for quasi invariant measures on homogeneous spaces)

Deitmar-Echterhoff: Principles of Harmonic Analysis (especially for the Selberg trace formula, structure of locally abelian groups and the measure theory part)

Barut and Raczka: The Theory of group representations and applications (For Mackey's theory of induced representation)

Montgomery, Zippin: Topological Transformation groups (Structure theory of locally compact groups and Hilbert 5th problem)

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The book

A first course in Harmonic Analysis

by Anton Deitmar has the noncommutative setting as one of its goals.

(check Gigapedia, you can get it over there).

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" Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion Groups " by Gregory S. Chirikjian and Alexander B. Kyatkin.

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