Group Representations and Harmonic Analysis from Euler to Langlands , Part II Anthony
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چکیده
T he essence of harmonic analysis is to decompose complicated expressions into pieces that reflect the structure of a group action when there is one. The goal is to make some difficult analysis manageable. In the seventeenth and eighteenth centuries, the groups that arose in this connection were the circle R/2πZ , the line R , and finite abelian groups. Embedded in applications were decompositions of functions in terms of multiplicative characters, continuous homomorphisms of the group into the nonzero complex numbers. In the case of the circle, the decomposition is just the expansion of a function on (−π,π ) into its Fourier series
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