Gideon R. Chiusole

Harmonic Analysis (HA) is the abstract incarnation of Fourier’s early attempts of considering a function as a sum of sin and cos terms (its harmonics) and using this representation to simplify linear PDE (originally the heat equation).

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In an effort to unify different versions of the classical Fourier transform on different function spaces, in the mid-20th century, the theory was generalized to locally compact abelian Hausdorff groups (LCAH).