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41-XX Approximations and expansions {For all approximation theory in the complex domain, see 30Exx, 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42Axx, 42A10 and 42A15; for numerical approximation, see 65Dxx} → ZMATH
41-00 General reference works (handbooks, dictionaries, bibliographies, etc.) → ZMATH
41-01 Instructional exposition (textbooks, tutorial papers, etc.) → ZMATH
41-02 Research exposition (monographs, survey articles) → ZMATH
41-03 Historical (must also be assigned at least one classification number from Section 01) → ZMATH
41-04 Explicit machine computation and programs (not the theory of computation or programming) → ZMATH
41-06 Proceedings, conferences, collections, etc. → ZMATH
41A05 Interpolation [See also 42A15 and 65D05] → ZMATH
41A10 Approximation by polynomials {For approximation by trigonometric polynomials, see 42A10} → ZMATH
41A15 Spline approximation → ZMATH
41A17 Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski\u\i-type inequalities) → ZMATH
41A20 Approximation by rational functions → ZMATH
41A21 Padé approximation → ZMATH
41A25 Rate of convergence, degree of approximation → ZMATH
41A27 Inverse theorems → ZMATH
41A28 Simultaneous approximation → ZMATH
41A29 Approximation with constraints → ZMATH
41A30 Approximation by other special function classes → ZMATH
41A35 Approximation by operators (in particular, by integral operators) → ZMATH
41A36 Approximation by positive operators → ZMATH
41A40 Saturation → ZMATH
41A44 Best constants → ZMATH
41A45 Approximation by arbitrary linear expressions → ZMATH
41A46 Approximation by arbitrary nonlinear expressions; widths and entropy → ZMATH
41A50 Best approximation, Chebyshev systems → ZMATH
41A52 Uniqueness of best approximation → ZMATH
41A55 Approximate quadratures → ZMATH
41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series) → ZMATH
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15] → ZMATH
41A63 Multidimensional problems (should also be assigned at least one other classification number in this section) → ZMATH
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) → ZMATH
41A80 Remainders in approximation formulas → ZMATH
41A99 Miscellaneous topics → ZMATH
Abel prize 2010
I. M. Gelfand 1913-2009

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