Essentials of the Fourier Transform
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
KeywordsSobolev Space Integral Operator Hardy Space Singular Integral Pseudodifferential Operator
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