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42-XX
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Fourier analysis
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|
42-00
|
General reference works (handbooks, dictionaries, bibliographies, etc.)
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|
42-01
|
Instructional exposition (textbooks, tutorial papers, etc.)
|
|
42-02
|
Research exposition (monographs, survey articles)
|
|
42-03
|
Historical {!must also be assigned at least one classification number from section 01}
|
|
42-04
|
Explicit machine computation and programs (not the theory of computation or programming)
|
|
42-06
|
Proceedings, conferences, collections, etc.
|
|
42Axx
|
Fourier analysis in one variable
|
|
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.)
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|
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
|
|
42Bxx
|
Fourier analysis in several variables
{For automorphic theory, see mainly
11F30}
|
|
42B05
|
Fourier series and coefficients
|
|
42B08
|
Summability
|
|
42B10
|
Fourier and Fourier - Stieltjes transforms and other transforms of Fourier type
|
|
42B15
|
Multipliers
|
|
42B20
|
Singular integrals (Caldersn - Zygmund, etc.)
|
|
42B25
|
Maximal functions, Littlewood - Paley theory
|
|
42B30
|
Hp-spaces
|
|
42B35
|
Function spaces arising in harmonic analysis
|
|
42B99
|
None of the above, but in this section
|
|
42Cxx
|
Nontrigonometric Fourier analysis
|
|
42C05
|
Orthogonal functions and polynomials, general theory
[See also
33C45,
33C50,
33D45]
|
|
42C10
|
Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
|
|
42C15
|
Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions
|
|
42C20
|
Rearrangements and other transformations of Fourier and other orthogonal series
|
|
42C25
|
Uniqueness and localization for orthogonal series
|
|
42C30
|
Completeness of sets of functions
|
|
42C40
|
Wavelets
|
|
42C99
|
None of the above, but in this section
|