| 42-XX | | Prev: 41 | Up: Top | Next: 43 | |
| Fourier analysis [xref: 30B50, 46F12] |
42-00
| General reference works (handbooks, dictionaries, bibliographies, etc.)
| 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
[xref: 41A05]
| 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
[xref: 44A05]
| 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
[xref: 47A57]
| 42A75 |
Classical almost periodic functions, mean periodic functions [See also 43A60]
| 42A82 |
Positive definite functions
[xref: 47A57]
| 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 (Calderón-Zygmund, etc.)
| 42B25 |
Maximal functions, Littlewood-Paley theory
| 42B30 |
$H^p$-spaces
[xref: 32A35, 46J15]
| 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
| |