Linked from

The 98 pages that link to Fourier series, each with the reason it gives.

• Uniform boundedness principleRelated: Uniform boundedness helps show that convergence of Fourier partial sums cannot hold everywhere for every continuous function.

• Abel's theorem (power series)Related: Abel-type limiting arguments also study Fourier sums through damping factors.

• Approximation theoryRelated: Fourier expansions approximate periodic functions using orthogonal frequency components.

• Bessel's inequalityRelated: Bessel’s inequality bounds the energy in any selected collection of Fourier coefficients.

• Parseval's theoremRelated: Its coefficients turn Parseval’s identity into a sum of spectral energies.

• Basel problemRelated: The Fourier series of x² gives a direct route to the sum.

• John Edensor LittlewoodRelated: Questions about convergence and summability of Fourier series connect directly to Littlewood’s analysis.

• Sine and cosineRelated: The functions form the basic components for decomposing periodic patterns.

• Pontryagin dualityRelated: The character viewpoint extends the frequency decomposition underlying Fourier series.

• Weierstrass M-testRelated: Coefficient bounds can let the M-test establish uniform convergence of a Fourier series.

• Abel's testRelated: Abel-type arguments help establish convergence properties of weighted Fourier sums.

• Even and odd functionsRelated: Parity eliminates either sine or cosine terms in many Fourier expansions.

• Peter–Weyl theoremRelated: On the circle group, Peter–Weyl becomes the familiar Fourier expansion.

• Vector-valued functionRelated: Its componentwise form can represent periodic vector-valued signals.

• Wirtinger's inequalityRelated: The inequality follows by bounding each nonconstant Fourier mode using its frequency.

• Abel's inequalityRelated: Abel-type estimates help control weighted trigonometric sums and convergence arguments.

• Cauchy's convergence testRelated: Cauchy estimates on partial sums help establish convergence in function spaces.

• Four-vertex theoremRelated: Fourier methods can express the support function and constrain how its curvature varies.

• Function of a real variableRelated: It decomposes suitable real-variable functions into simple oscillatory components.