42Axx

 40 | 42 | 42B

Fourier analysis in one variable

42A05Trigonometric polynomials, inequalities, extremal problems
42A10Trigonometric approximation
42A15Trigonometric interpolation
42A16Fourier coefficients, Fourier series of functions with special properties, special Fourier series
{For automorphic theory, see mainly 11F30}
42A20Convergence and absolute convergence of Fourier and trigonometric series
42A24Summability and absolute summability of Fourier and trigonometric series
42A32Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
42A38Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42A45Multipliers
42A50Conjugate functions, conjugate series, singular integrals
42A55Lacunary series of trigonometric and other functions; Riesz products
42A61Probabilistic methods
42A63Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization
42A65Completeness of sets of functions
42A70Trigonometric moment problems
42A75Classical almost periodic functions, mean periodic functions
[See also 43A60]
42A82Positive definite functions
42A85Convolution, factorization
42A99None of the above, but in this section