The nature of Fourier analysis on the circle T is determined by the collection of characters on the circle: these are the continuous, multiplicative homomorphisms of T into T itself—namely the functions t↦ eint for n∈ ℤ. The Peter–Weyl theorem tells us that a viable Fourier analysis may be built on these characters
CITATION STYLE
Krantz, S. G. (2009). Essentials of the Fourier Transform. In Applied and Numerical Harmonic Analysis (pp. 35–47). Springer International Publishing. https://doi.org/10.1007/978-0-8176-4669-1_3
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