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Mathematical Sciences Classification System

42Axx - Harmonic analysis in one variable

• 3
  42A05
  Trigonometric polynomials, inequalities, extremal problems
• 8
  42A10
  Trigonometric approximation
• 42A15
  Trigonometric interpolation
• 6
  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.)
• 22
  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