Mathematical Sciences Classification System

42Axx - Harmonic analysis in one variable

  • 2
    42A05
    Trigonometric polynomials, inequalities, extremal problems
  • 8
    42A10
    Trigonometric approximation
  • 42A15
    Trigonometric interpolation
  • 5
    42A16
    Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly 11F30}
  • 1
    42A20
    Convergence and absolute convergence of Fourier and trigonometric series
  • 2
    42A24
    Summability and absolute summability of Fourier and trigonometric series
  • 42A32
    Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
  • 20
    42A38
    Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
  • 1
    42A45
    Multipliers
  • 42A50
    Conjugate functions, conjugate series, singular integrals
  • 1
    42A55
    Lacunary series of trigonometric and other functions; Riesz products
  • 1
    42A61
    Probabilistic methods
  • 42A63
    Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization
  • 3
    42A65
    Completeness of sets of functions
  • 1
    42A70
    Trigonometric moment problems
  • 1
    42A75
    Classical almost periodic functions, mean periodic functions [See also 43A60]
  • 3
    42A82
    Positive definite functions
  • 42A85
    Convolution, factorization
  • 2
    42A99
    None of the above, but in this section

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