41A20 Approximation by rational functions

41A25 Rate of convergence, degree of approximation

41A30 Approximation by other special function classes

41A35 Approximation by operators (in particular, by integral operators)

41A36 Approximation by positive operators

41A45 Approximation by arbitrary linear expressions

41A46 Approximation by arbitrary nonlinear expressions; widths and entropy

41A50 Best approximation, Chebyshev systems

41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)

41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also <a href="#code:30E15">30E15</a>]

41A63 Multidimensional problems (should also be assigned at least one other classification number in this section)

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

41A80 Remainders in approximation formulas

41A99 None of the above, but in this section

42-XX Harmonic analysis on Euclidean spaces

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.

42A05 Trigonometric polynomials, inequalities, extremal problems

42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly <a href="#code:11F30">11F30</a>}

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

42A50 Conjugate functions, conjugate series, singular integrals