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

• Linear differential equationRelated: Linear equations often let each Fourier mode evolve independently.

• Spectral methodRelated: It supplies the standard basis for periodic spectral approximations.

• ConvergenceBroader topic: Different notions of convergence govern whether its partial sums recover the function.

• Convergence of a seriesRelated: Different notions of convergence govern its pointwise and mean-square behavior.

• Fourier coefficientNarrower topic: Fourier coefficients are the weights that assemble its frequency components.

• Separation of variablesRelated: Fourier series combine separated modes to fit many initial or boundary profiles.

• Cesàro summationRelated: Cesàro summation became useful for assigning limits to Fourier series that fail to converge pointwise.

• Gibbs phenomenonNarrower topic: The phenomenon arises when a Fourier series is cut off at a finite number of terms.

• Spectral theoremRelated: It exemplifies spectral expansion in an orthogonal basis of eigenfunctions.

• Trigonometric identityRelated: Trigonometric identities help manipulate the periodic terms in these expansions.

• HarmonicRelated: It expresses periodic waveforms as sums of harmonics.

• Legendre polynomialsCompared with: Fourier modes handle periodic geometry, while Legendre modes suit interval and spherical-coordinate problems.

• Taylor polynomialCompared with: Fourier approximation uses periodic basis functions rather than powers centered at one point.

• Convergent seriesRelated: Its pointwise and function-space convergence connect series limits to signal representation.

• Kronecker deltaRelated: Orthogonality of its discrete modes yields Kronecker-delta relations.

• Nearly-free-electron modelRelated: Fourier components of the crystal potential couple electron states differing by reciprocal-lattice vectors.

• Poisson summation formulaRelated: Periodizing a function produces a Fourier series whose coefficients are transform samples.

• Sturm–Liouville theoryRelated: It is a familiar orthogonal expansion that generalizes to Sturm–Liouville eigenfunctions.

• Peter Gustav Lejeune DirichletRelated: Dirichlet’s work helped clarify when such series converge to a function.

• Theta functionRelated: Theta functions are rapidly convergent Fourier-type series in their elliptic variable.

• 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 identityNarrower topic: For periodic functions, the identity equates the integral of squared magnitude with the sum of squared Fourier coefficients.

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

• Riemann–Lebesgue lemmaNarrower topic: The lemma constrains coefficients but does not ensure that the series converges to the function.

• Spectral analysisCompared with: It describes periodic functions, while spectral analysis also handles finite and nonperiodic data.

• 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.

• Fejér's theoremNarrower topic: The theorem concerns convergence of averaged partial sums of this expansion.

• 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.

• Dirichlet–Jordan testNarrower topic: The test specifies pointwise convergence of these expansions under bounded variation.

• 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.

• Dini testNarrower topic: The Dini test gives a sufficient condition for this series to converge at a specified point.

• F. and M. Riesz theoremNarrower topic: Questions about one-sided frequency content in Fourier series motivate the theorem's measure formulation.

• 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.

• Kosambi–Karhunen–Loève theoremCompared with: Fourier modes are fixed by periodic geometry, whereas covariance eigenfunctions adapt to the process.

• Series expansionBroader topic: It expands functions in oscillatory basis terms rather than powers.