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

• Vector spaceRelated: Fourier analysis represents functions using linear combinations of basis functions.

• Uniform convergenceRelated: Uniform convergence criteria determine when Fourier partial sums approximate a function uniformly.

• Heat equationRelated: Fourier used trigonometric expansions to solve heat-conduction problems.

• Wave equationRelated: Periodic wave solutions can be decomposed into independent oscillatory modes.

• Georg CantorRelated: Questions about uniqueness of these expansions formed the setting for Cantor’s early research.

• Simple harmonic motionRelated: It extends the role of sinusoidal motion to more complex periodic waveforms.

• Laplace's equationRelated: Fourier expansions encode boundary data and allow harmonic solutions to be built mode by mode.

• Real analysisRelated: Convergence analysis determines when these trigonometric expansions represent their functions.

• Inner productRelated: Orthogonality of sine and cosine modes lets inner products extract Fourier coefficients.

• Harmonic seriesRelated: It explains how a periodic waveform can be decomposed into harmonics.

• Dot productRelated: Integrals of products of basis functions act like dot products and extract coefficients.

• Pointwise convergenceRelated: Questions about convergence at each point are central to interpreting Fourier series.

• SineRelated: Sine functions serve as basic components for decomposing periodic signals.

• Nyquist–Shannon sampling theoremRelated: It introduces frequency-based descriptions used to reason about sampling.

• Periodic functionRelated: Its harmonics encode a function’s repetition through integer multiples of a base frequency.

• Partial sumRelated: Finite partial sums provide trigonometric approximations to the represented function.

• Spherical harmonicsRelated: Spherical harmonics extend Fourier’s orthogonal-basis idea from a circle to a sphere.

• Trigonometric functionsRelated: It uses trigonometric functions as building blocks for analyzing periodic signals.

• Absolute convergenceRelated: Absolute convergence gives Fourier series stronger stability than ordinary pointwise convergence.

• Linear combinationRelated: Finite Fourier approximations are linear combinations of basis functions.

• Complex exponentialRelated: Complex exponentials compactly represent the sine and cosine harmonics.

• Fundamental frequencyRelated: It expresses periodic waveforms through harmonics whose spacing reveals the repetition rate.

• OrthogonalityRelated: Sines and cosines form orthogonal families under suitable integral inner products.

• Reciprocal latticeRelated: Periodic crystal density has Fourier components at reciprocal-lattice vectors.

• Orthogonal projectionRelated: Truncated Fourier sums are projections onto finite-dimensional spaces of trigonometric functions.

• CoefficientRelated: Its coefficients specify the amplitudes of the component frequencies.

• Conditional convergenceRelated: Fourier coefficients can produce pointwise convergent series that are not absolutely convergent.

• Spatial frequencyRelated: It explains how complex repeating patterns contain multiple spatial frequencies.

• Karl WeierstrassRelated: Questions about convergence of trigonometric series helped motivate rigorous study of function behavior.

• Orthonormal basisRelated: Trigonometric orthonormal bases turn functions into convergent sums of frequency components.

• CosineRelated: Cosine terms encode the even oscillatory components of periodic signals.

• Complete metric spaceRelated: Completeness of function spaces helps establish convergence and representation results for Fourier expansions.

• Inner product spaceRelated: Orthogonality of sine and cosine functions determines Fourier coefficients.

• Periodic boundary conditionRelated: Periodic endpoint matching makes Fourier series a natural representation for many solutions.

• Almost-everywhere convergenceRelated: Convergence of Fourier partial sums is often studied almost everywhere rather than at every point.

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

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

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

• 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.

• 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.

• 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.