harmonic analysis

Non-commutative harmonic analysis: quantum Fourier transform

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In the contemporary mathematical landscape, non-commutative harmonic analysis stands out as a major discipline, breaking the boundaries of classical harmonic analysis developed since the 18th century. This branch refines its sophistication by directing its tools towards algebraic structures where commutativity is absent, thus offering unprecedented perspectives in quantum mechanics and beyond. The quantum Fourier transform … Read more

Harmonic analysis: generalized Fourier transforms

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Harmonic analysis represents a fundamental advance in mathematics, offering a powerful key to understanding, decomposing, and studying complex functions and signals. Originating from Fourier series, this field has evolved to include generalized Fourier transforms, allowing for the analysis of not only periodic signals but also a vast array of non-periodic signals in many contexts. This … Read more