La Classification Mathématique par matières 2000
Mathematics subject Classification 2000

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46-XX Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx]

• 46-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 46-01 Instructional exposition (textbooks, tutorial papers, etc.)
• 46-02 Research exposition (monographs, survey articles)
• 46-03 Historical (must also be assigned at least one classification number from Section 01)
• 46-04 Explicit machine computation and programs (not the theory of computation or programming)
• 46-06 Proceedings, conferences, collections, etc.
• 46-99 Functional analysis (not classified at a more specific level)
• 46Axx Topological linear spaces and related structures [For function spaces, see 46Exx]
• 46Bxx Normed linear spaces and Banach spaces; Banach lattices [For function spaces, see 46Exx]
• 46Cxx Inner product spaces and their generalizations, Hilbert spaces [For function spaces, see 46Exx]
• 46Exx Linear function spaces and their duals [See also 30H05, 32A38, 46F05] [For function algebras, see 46J10]
  • 46E05 Lattices of continuous, differentiable or analytic functions
  • 46E10 Topological linear spaces of continuous, differentiable or analytic functions
  • 46E15 Banach spaces of continuous, differentiable or analytic functions
  • 46E20 Hilbert spaces of continuous, differentiable or analytic functions
  • 46E22 Hilbert spaces with reproducing kernels (=[proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]
  • 46E25 Rings and algebras of continuous, differentiable or analytic functions [For Banach function algebras, see 46J10, 46J15]
  • 46E27 Spaces of measures [See also 28A33, 46Gxx]
  • 46E30 Spaces of measurable functions (L^p-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
  • 46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
  • 46E39 Sobolev (and similar kinds of) spaces of functions of discrete variables
  • 46E40 Spaces of vector- and operator-valued functions
  • 46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20, 46G25, 47H60]
  • 46E99 None of the above, but in this section
• 46Fxx Distributions, generalized functions, distribution spaces [See also 46T30]
• 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx]
• 46Hxx Topological algebras, normed rings and algebras, Banach algebras [For group algebras, convolution algebras and measure algebras, see 43A10, 43A20]
• 46Jxx Commutative Banach algebras and commutative topological algebras [See also 46E25]
• 46Kxx Topological (rings and) algebras with an involution [See also 16W10]
• 46Lxx Selfadjoint operator algebras (C^*-algebras, von Neumann (W*-) algebras, etc.) [See also 22D25, 47Lxx]
• 46Mxx Methods of category theory in functional analysis [See also 18-XX]
• 46Nxx Miscellaneous applications of functional analysis [See also 47Nxx]
• 46Sxx Other (nonclassical) types of functional analysis [See also 47Sxx]
• 46Txx Nonlinear functional analysis [See also 47Hxx, 47Jxx, 58Cxx, 58Dxx]

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