Parseval's identity

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Parseval's identity. 1 connected concept: Hilbert space (related to).

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Summary

In mathematical analysis, Parseval's identity, named after Marc-Antoine Parseval, is a fundamental result on the summability of the Fourier series of a function.

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Equality condition for orthonormal expansions
In a Hilbert space, Parseval's identity generalizes the Pythagorean theorem to infinite-dimensional spaces, relating the norm of a vector to its coefficients in an orthonormal basis.
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