Bessel's inequality

For an orthonormal sequence

(e_{n})

in a Hilbert space,

\sum_{n} ∣ ⟨ x, e_{n} ⟩ ∣^{2} \leq ∥ x ∥^{2} .

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Absolute Fourier convergence from a square-integrable derivative
Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 8 / 1 / iv / Solution
Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 8 / 1 / vii / Solution
Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 8 / 1 / v / Solution
Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 326 / 1 / iii / Solution
Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 335 / 3 / b / Solution
Sampling expansion by periodic Fourier projection

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