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Functional analysis --- Banach [Algebra's van ] --- Banach [Algebres de ] --- Banach [Espaces de ] --- Banach [Ruimten van ] --- Banach algebras --- Banach spaces --- Banach spaces. --- Ideals (Algebra) --- Approximation theory. --- 51 --- Approximation theory --- Theory of approximation --- Functions --- Polynomials --- Chebyshev systems --- Algebraic ideals --- Algebraic fields --- Rings (Algebra) --- Functions of complex variables --- Generalized spaces --- Topology --- Mathematics --- 51 Mathematics

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Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.

Algebraic geometry --- Ordered algebraic structures --- Associative rings --- Abelian groups --- Functor theory --- Anneaux associatifs --- Groupes abéliens --- Foncteurs, Théorie des --- 512.73 --- 515.14 --- Functorial representation --- Algebra, Homological --- Categories (Mathematics) --- Functional analysis --- Transformations (Mathematics) --- Commutative groups --- Group theory --- Rings (Algebra) --- Cohomology theory of algebraic varieties and schemes --- Algebraic topology --- Abelian groups. --- Associative rings. --- Functor theory. --- 515.14 Algebraic topology --- 512.73 Cohomology theory of algebraic varieties and schemes --- Groupes abéliens --- Foncteurs, Théorie des --- Abelian group. --- Absolute value. --- Addition. --- Algebraic K-theory. --- Algebraic equation. --- Algebraic integer. --- Banach algebra. --- Basis (linear algebra). --- Big O notation. --- Circle group. --- Coefficient. --- Commutative property. --- Commutative ring. --- Commutator. --- Complex number. --- Computation. --- Congruence subgroup. --- Coprime integers. --- Cyclic group. --- Dedekind domain. --- Direct limit. --- Direct proof. --- Direct sum. --- Discrete valuation. --- Division algebra. --- Division ring. --- Elementary matrix. --- Elliptic function. --- Exact sequence. --- Existential quantification. --- Exterior algebra. --- Factorization. --- Finite group. --- Free abelian group. --- Function (mathematics). --- Fundamental group. --- Galois extension. --- Galois group. --- General linear group. --- Group extension. --- Hausdorff space. --- Homological algebra. --- Homomorphism. --- Homotopy. --- Ideal (ring theory). --- Ideal class group. --- Identity element. --- Identity matrix. --- Integral domain. --- Invertible matrix. --- Isomorphism class. --- K-theory. --- Kummer theory. --- Lattice (group). --- Left inverse. --- Local field. --- Local ring. --- Mathematics. --- Matsumoto's theorem. --- Maximal ideal. --- Meromorphic function. --- Monomial. --- Natural number. --- Noetherian. --- Normal subgroup. --- Number theory. --- Open set. --- Picard group. --- Polynomial. --- Prime element. --- Prime ideal. --- Projective module. --- Quadratic form. --- Quaternion. --- Quotient ring. --- Rational number. --- Real number. --- Right inverse. --- Ring of integers. --- Root of unity. --- Schur multiplier. --- Scientific notation. --- Simple algebra. --- Special case. --- Special linear group. --- Subgroup. --- Summation. --- Surjective function. --- Tensor product. --- Theorem. --- Topological K-theory. --- Topological group. --- Topological space. --- Topology. --- Torsion group. --- Variable (mathematics). --- Vector space. --- Wedderburn's theorem. --- Weierstrass function. --- Whitehead torsion. --- K-théorie

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The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.

Harmonic analysis. --- Harmonic functions. --- Functions, Harmonic --- Laplace's equations --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Harmonic analysis. Fourier analysis --- Harmonic analysis --- Fourier analysis --- Harmonic functions --- Analyse harmonique --- Analyse de Fourier --- Fonctions harmoniques --- Fourier Analysis --- Fourier, Transformations de --- Euclide, Espaces d' --- Bessel functions --- Differential equations, Partial --- Fourier series --- Lamé's functions --- Spherical harmonics --- Toroidal harmonics --- Banach algebras --- Time-series analysis --- Analysis, Fourier --- Fourier analysis. --- Basic Sciences. Mathematics --- Analysis, Functions --- Analysis, Functions. --- Calculus --- Mathematical analysis --- Mathematics --- Fourier, Transformations de. --- Euclide, Espaces d'. --- Potentiel, Théorie du --- Fonctions harmoniques. --- Potential theory (Mathematics) --- Analytic continuation. --- Analytic function. --- Banach algebra. --- Banach space. --- Bessel function. --- Borel measure. --- Boundary value problem. --- Bounded operator. --- Bounded set (topological vector space). --- Cartesian coordinate system. --- Cauchy–Riemann equations. --- Change of variables. --- Characteristic function (probability theory). --- Characterization (mathematics). --- Complex plane. --- Conformal map. --- Conjugate transpose. --- Continuous function (set theory). --- Continuous function. --- Convolution. --- Differentiation of integrals. --- Dimensional analysis. --- Dirichlet problem. --- Disk (mathematics). --- Distribution (mathematics). --- Equation. --- Euclidean space. --- Existential quantification. --- Fourier inversion theorem. --- Fourier series. --- Fourier transform. --- Fubini's theorem. --- Function (mathematics). --- Function space. --- Green's theorem. --- Hardy's inequality. --- Hardy–Littlewood maximal function. --- Harmonic function. --- Hermitian matrix. --- Hilbert transform. --- Holomorphic function. --- Homogeneous function. --- Inequality (mathematics). --- Infimum and supremum. --- Interpolation theorem. --- Interval (mathematics). --- Lebesgue integration. --- Lebesgue measure. --- Linear interpolation. --- Linear map. --- Linear space (geometry). --- Line–line intersection. --- Liouville's theorem (Hamiltonian). --- Lipschitz continuity. --- Locally integrable function. --- Lp space. --- Majorization. --- Marcinkiewicz interpolation theorem. --- Mean value theorem. --- Measure (mathematics). --- Mellin transform. --- Monotonic function. --- Multiplication operator. --- Norm (mathematics). --- Operator norm. --- Orthogonal group. --- Paley–Wiener theorem. --- Partial derivative. --- Partial differential equation. --- Plancherel theorem. --- Pointwise convergence. --- Poisson kernel. --- Poisson summation formula. --- Polynomial. --- Principal value. --- Quadratic form. --- Radial function. --- Radon–Nikodym theorem. --- Representation theorem. --- Riesz transform. --- Scientific notation. --- Series expansion. --- Singular integral. --- Special case. --- Subharmonic function. --- Support (mathematics). --- Theorem. --- Topology. --- Total variation. --- Trigonometric polynomial. --- Trigonometric series. --- Two-dimensional space. --- Union (set theory). --- Unit disk. --- Unit sphere. --- Upper half-plane. --- Variable (mathematics). --- Vector space. --- Fourier, Analyse de --- Potentiel, Théorie du. --- Potentiel, Théorie du --- Espaces de hardy