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42Axx FourierHarmonic analysis in one variable {Info & Stats}

  • 42A05 Trigonometric polynomials, inequalities, extremal problems
  • 42A10 Trigonometric approximation
  • 42A15 Trigonometric interpolation
  • 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly 11F30}
  • 42A20 Convergence and absolute convergence of Fourier and trigonometric series
  • 42A24 Summability and absolute summability of Fourier and trigonometric series
  • 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
  • 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
  • 42A45 Multipliers
  • 42A50 Conjugate functions, conjugate series, singular integrals
  • 42A55 Lacunary series of trigonometric and other functions; Riesz products
  • 42A61 Probabilistic methods
  • 42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization
  • 42A65 Completeness of sets of functions
  • 42A70 Trigonometric moment problems
  • 42A75 Classical almost periodic functions, mean periodic functions [See also 43A60]
  • 42A82 Positive definite functions
  • 42A85 Convolution, factorization
  • 42A99 None of the above, but in this section