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

• Fourier transformCompared with: It handles periodic functions through discrete harmonics, unlike the transform’s continuous frequency representation.

• Hilbert spaceBroader topic: Fourier coefficients are inner products with an orthogonal family in a function space.

• Taylor seriesCompared with: Fourier series use global periodic basis functions rather than powers centered at one point.

• 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.

• Generating functionCompared with: Unlike coefficient-encoding formal series, it represents functions through frequency components.

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

• Power seriesCompared with: It uses periodic basis functions rather than successive powers of a variable.

• Fourier analysisBroader topic: It decomposes periodic functions into discrete harmonics.

• 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.

• Infinite seriesBroader topic: Convergence of its partial sums governs approximation of periodic signals.

• 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.

• Polynomial interpolationCompared with: Fourier interpolation uses periodic trigonometric basis functions rather than algebraic polynomials.

• 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.

• PhasorCompared with: A single phasor describes one frequency component, while a Fourier series combines many.

• Laplace transformCompared with: Fourier series target periodic behavior, unlike Laplace methods' common use for initial-value problems.

• Taylor's theoremCompared with: It represents global periodic behavior rather than local behavior from derivatives at one point.

• 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.

• InterpolationCompared with: Fourier methods reconstruct periodic signals through frequency components rather than local point-to-point rules.

• 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.

• Harmonic analysisBroader topic: It decomposes periodic functions into discrete oscillatory components.

• Joseph FourierBroader topic: Fourier used these expansions to describe temperature distributions in his theory of heat.

• Dirichlet seriesCompared with: Fourier series expand periodic functions in frequencies rather than encode coefficients through n⁻ˢ.

• 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.