Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.

Algebraic geometry --- Algebraïsche meetkunde --- Geometry [Algebraic ] --- Géométrie algébrique --- Meetkunde [Algebraïsche ] --- Riemann-Roch theorema's --- Riemann-Roch thoerems --- Theoremes de Riemann-Roch --- Geometry, Algebraic. --- Riemann-Roch theorems. --- Theorems, Riemann-Roch --- Algebraic functions --- Geometry, Algebraic --- Geometry --- Addition. --- Adjoint. --- Alexander Grothendieck. --- Algebraic geometry. --- Analytic torsion. --- Arakelov theory. --- Asymptote. --- Asymptotic expansion. --- Asymptotic formula. --- Big O notation. --- Cartesian coordinate system. --- Characteristic class. --- Chern class. --- Chow group. --- Closed immersion. --- Codimension. --- Coherent sheaf. --- Cohomology. --- Combination. --- Commutator. --- Computation. --- Covariant derivative. --- Curvature. --- Derivative. --- Determinant. --- Diagonal. --- Differentiable manifold. --- Differential form. --- Dimension (vector space). --- Divisor. --- Domain of a function. --- Dual basis. --- E6 (mathematics). --- Eigenvalues and eigenvectors. --- Embedding. --- Endomorphism. --- Exact sequence. --- Exponential function. --- Generic point. --- Heat kernel. --- Injective function. --- Intersection theory. --- K-group. --- Levi-Civita connection. --- Line bundle. --- Linear algebra. --- Local coordinates. --- Mathematical induction. --- Morphism. --- Natural number. --- Neighbourhood (mathematics). --- Parameter. --- Projective space. --- Pullback (category theory). --- Pullback (differential geometry). --- Pullback. --- Riemannian manifold. --- Riemann–Roch theorem. --- Self-adjoint operator. --- Smoothness. --- Sobolev space. --- Stochastic calculus. --- Summation. --- Supertrace. --- Theorem. --- Transition function. --- Upper half-plane. --- Vector bundle. --- Volume form.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Polynomials play a crucial role in many areas of mathematics including algebra, analysis, number theory, and probability theory. They also appear in physics, chemistry, and economics. Especially extensively studied are certain infinite families of polynomials. Here, we only mention some examples: Bernoulli, Euler, Gegenbauer, trigonometric, and orthogonal polynomials and their generalizations. There are several approaches to these classical mathematical objects. This Special Issue presents nine high quality research papers by leading researchers in this field. I hope the reading of this work will be useful for the new generation of mathematicians and for experienced researchers as well

Research & information: general --- Mathematics & science --- Shivley’s matrix polynomials --- Generating matrix functions --- Matrix recurrence relations --- summation formula --- Operational representations --- Euler polynomials --- higher degree equations --- degenerate Euler numbers and polynomials --- degenerate q-Euler numbers and polynomials --- degenerate Carlitz-type (p, q)-Euler numbers and polynomials --- 2D q-Appell polynomials --- twice-iterated 2D q-Appell polynomials --- determinant expressions --- recurrence relations --- 2D q-Bernoulli polynomials --- 2D q-Euler polynomials --- 2D q-Genocchi polynomials --- Apostol type Bernoulli --- Euler and Genocchi polynomials --- Euler numbers and polynomials --- Carlitz-type degenerate (p,q)-Euler numbers and polynomials --- Carlitz-type higher-order degenerate (p,q)-Euler numbers and polynomials --- symmetric identities --- (p, q)-cosine Bernoulli polynomials --- (p, q)-sine Bernoulli polynomials --- (p, q)-numbers --- (p, q)-trigonometric functions --- Bernstein operators --- rate of approximation --- Voronovskaja type asymptotic formula --- q-cosine Euler polynomials --- q-sine Euler polynomials --- q-trigonometric function --- q-exponential function --- multiquadric --- radial basis function --- radial polynomials --- the shape parameter --- meshless --- Kansa method --- Shivley’s matrix polynomials --- Generating matrix functions --- Matrix recurrence relations --- summation formula --- Operational representations --- Euler polynomials --- higher degree equations --- degenerate Euler numbers and polynomials --- degenerate q-Euler numbers and polynomials --- degenerate Carlitz-type (p, q)-Euler numbers and polynomials --- 2D q-Appell polynomials --- twice-iterated 2D q-Appell polynomials --- determinant expressions --- recurrence relations --- 2D q-Bernoulli polynomials --- 2D q-Euler polynomials --- 2D q-Genocchi polynomials --- Apostol type Bernoulli --- Euler and Genocchi polynomials --- Euler numbers and polynomials --- Carlitz-type degenerate (p,q)-Euler numbers and polynomials --- Carlitz-type higher-order degenerate (p,q)-Euler numbers and polynomials --- symmetric identities --- (p, q)-cosine Bernoulli polynomials --- (p, q)-sine Bernoulli polynomials --- (p, q)-numbers --- (p, q)-trigonometric functions --- Bernstein operators --- rate of approximation --- Voronovskaja type asymptotic formula --- q-cosine Euler polynomials --- q-sine Euler polynomials --- q-trigonometric function --- q-exponential function --- multiquadric --- radial basis function --- radial polynomials --- the shape parameter --- meshless --- Kansa method

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, Lsup estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.

Harmonic analysis. Fourier analysis --- Harmonic analysis --- Analyse harmonique --- Harmonic analysis. --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Groupe de Heisenberg. --- Addition. --- Analytic function. --- Asymptote. --- Asymptotic analysis. --- Asymptotic expansion. --- Asymptotic formula. --- Automorphism. --- Axiom. --- Banach space. --- Bessel function. --- Big O notation. --- Bilinear form. --- Borel measure. --- Boundary value problem. --- Bounded function. --- Bounded mean oscillation. --- Bounded operator. --- Boundedness. --- Cancellation property. --- Cauchy's integral theorem. --- Cauchy–Riemann equations. --- Characteristic polynomial. --- Characterization (mathematics). --- Commutative property. --- Commutator. --- Complex analysis. --- Convolution. --- Differential equation. --- Differential operator. --- Dimension (vector space). --- Dimension. --- Dirac delta function. --- Dirichlet problem. --- Elliptic operator. --- Existential quantification. --- Fatou's theorem. --- Fourier analysis. --- Fourier integral operator. --- Fourier inversion theorem. --- Fourier series. --- Fourier transform. --- Fubini's theorem. --- Function (mathematics). --- Fundamental solution. --- Gaussian curvature. --- Hardy space. --- Harmonic function. --- Heisenberg group. --- Hilbert space. --- Hilbert transform. --- Holomorphic function. --- Hölder's inequality. --- Infimum and supremum. --- Integral transform. --- Interpolation theorem. --- Lagrangian (field theory). --- Laplace's equation. --- Lebesgue measure. --- Lie algebra. --- Line segment. --- Linear map. --- Lipschitz continuity. --- Locally integrable function. --- Marcinkiewicz interpolation theorem. --- Martingale (probability theory). --- Mathematical induction. --- Maximal function. --- Meromorphic function. --- Multiplication operator. --- Nilpotent Lie algebra. --- Norm (mathematics). --- Number theory. --- Operator theory. --- Order of integration (calculus). --- Orthogonality. --- Oscillatory integral. --- Poisson summation formula. --- Projection (linear algebra). --- Pseudo-differential operator. --- Pseudoconvexity. --- Rectangle. --- Riesz transform. --- Several complex variables. --- Sign (mathematics). --- Singular integral. --- Sobolev space. --- Special case. --- Spectral theory. --- Square (algebra). --- Stochastic differential equation. --- Subharmonic function. --- Submanifold. --- Summation. --- Support (mathematics). --- Theorem. --- Translational symmetry. --- Uniqueness theorem. --- Variable (mathematics). --- Vector field. --- Fourier, Analyse de --- Fourier, Opérateurs intégraux de

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Based on seven lecture series given by leading experts at a summer school at Peking University, in Beijing, in 1984. this book surveys recent developments in the areas of harmonic analysis most closely related to the theory of singular integrals, real-variable methods, and applications to several complex variables and partial differential equations. The different lecture series are closely interrelated; each contains a substantial amount of background material, as well as new results not previously published. The contributors to the volume are R. R. Coifman and Yves Meyer, Robert Fcfferman,Carlos K. Kenig, Steven G. Krantz, Alexander Nagel, E. M. Stein, and Stephen Wainger.

Harmonic analysis. --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Analytic function. --- Asymptotic formula. --- Bergman metric. --- Bernhard Riemann. --- Bessel function. --- Biholomorphism. --- Boundary value problem. --- Bounded mean oscillation. --- Bounded operator. --- Boundedness. --- Cauchy's integral formula. --- Characteristic function (probability theory). --- Characterization (mathematics). --- Coefficient. --- Commutator. --- Complexification (Lie group). --- Continuous function. --- Convolution. --- Degeneracy (mathematics). --- Differential equation. --- Differential operator. --- Dirac delta function. --- Dirichlet problem. --- Equation. --- Estimation. --- Existence theorem. --- Existential quantification. --- Explicit formula. --- Explicit formulae (L-function). --- Fatou's theorem. --- Fourier analysis. --- Fourier integral operator. --- Fourier transform. --- Fredholm theory. --- Fubini's theorem. --- Function (mathematics). --- Functional calculus. --- Fundamental solution. --- Gaussian curvature. --- Hardy space. --- Harmonic function. --- Harmonic measure. --- Heisenberg group. --- Hilbert space. --- Hilbert transform. --- Hodge theory. --- Holomorphic function. --- Hyperbolic partial differential equation. --- Hölder's inequality. --- Infimum and supremum. --- Integration by parts. --- Interpolation theorem. --- Intersection (set theory). --- Invertible matrix. --- Isometry group. --- Laplace operator. --- Laplace's equation. --- Lebesgue measure. --- Linear map. --- Lipschitz continuity. --- Lipschitz domain. --- Lp space. --- Mathematical induction. --- Mathematical physics. --- Maximal function. --- Maximum principle. --- Measure (mathematics). --- Newtonian potential. --- Non-Euclidean geometry. --- Number theory. --- Operator theory. --- Oscillatory integral. --- Parameter. --- Partial derivative. --- Partial differential equation. --- Polynomial. --- Power series. --- Product metric. --- Radon–Nikodym theorem. --- Riemannian manifold. --- Riesz representation theorem. --- Scientific notation. --- Several complex variables. --- Sign (mathematics). --- Simultaneous equations. --- Singular function. --- Singular integral. --- Sobolev space. --- Square (algebra). --- Statistical hypothesis testing. --- Stokes' theorem. --- Support (mathematics). --- Tangent space. --- Tensor product. --- Theorem. --- Trigonometric series. --- Uniformization theorem. --- Variable (mathematics). --- Vector field.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Singularities of solutions of differential equations forms the common theme of these papers taken from a seminar held at the Institute for Advanced Study in Princeton in 1977-1978. While some of the lectures were devoted to the analysis of singularities, others focused on applications in spectral theory. As an introduction to the subject, this volume treats current research in the field in such a way that it can be studied with profit by the non-specialist.

Partial differential equations --- Differential equations, Linear --- Differential equations, Partial --- Equations différentielles linéaires --- Equations aux dérivées partielles --- Numerical solutions --- Congresses --- Solutions numériques --- Congrès --- Théorie asymptotique --- 517.95 --- -Differential equations, Partial --- -Partial differential equations --- Linear differential equations --- Linear systems --- Insect societies. --- Insects --- Congresses. --- Ecology. --- 517.95 Partial differential equations --- -517.95 Partial differential equations --- Equations différentielles linéaires --- Equations aux dérivées partielles --- Solutions numériques --- Congrès --- Théorie asymptotique --- -Hexapoda --- Insecta --- Pterygota --- Arthropoda --- Entomology --- Behavior, Animal --- Ecology --- Insecta. --- Insect societies --- Sociétés d'insectes --- Insectes --- Ecologie --- Numerical solutions&delete& --- Insects, Social --- Social insects --- Animal societies --- Behavior --- Insects. Springtails --- Animal ethology and ecology. Sociobiology --- Behavior, Animal. --- Équations aux dérivées partielles --- Solutions numériques. --- A priori estimate. --- Adjoint equation. --- Analytic continuation. --- Analytic function. --- Analytic manifold. --- Asymptote. --- Asymptotic analysis. --- Asymptotic distribution. --- Asymptotic expansion. --- Asymptotic formula. --- Big O notation. --- Calculus on manifolds. --- Canonical transformation. --- Characteristic equation. --- Characteristic function (probability theory). --- Codimension. --- Cohomology. --- Commutator. --- Complex manifold. --- Complex number. --- Continuous function (set theory). --- Continuous function. --- Covariant derivative. --- Diffeomorphism. --- Differential equation. --- Differential operator. --- Dirichlet problem. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Elementary proof. --- Elliptic boundary value problem. --- Equation. --- Equivalence class. --- Equivalence relation. --- Error term. --- Existence theorem. --- Existential quantification. --- Exponential function. --- Fourier integral operator. --- Fourier inversion theorem. --- Fourier transform. --- Functional calculus. --- Fundamental solution. --- Hamiltonian vector field. --- Hardy space. --- Harmonic analysis. --- Hermann Weyl. --- Hermitian adjoint. --- Hilbert space. --- Holomorphic function. --- Homogeneous function. --- Hyperbolic partial differential equation. --- Hyperfunction. --- Hypersurface. --- Inclusion map. --- Inequality (mathematics). --- Integer lattice. --- Integral transform. --- Irreducible representation. --- Lagrangian (field theory). --- Laplace operator. --- Limit (mathematics). --- Linear map. --- Local diffeomorphism. --- Manifold. --- Mathematical optimization. --- Maximal torus. --- Monotonic function. --- Ordinary differential equation. --- Oscillatory integral. --- Partial differential equation. --- Partition of unity. --- Poisson bracket. --- Poisson summation formula. --- Polynomial. --- Projection (linear algebra). --- Projective variety. --- Pseudo-differential operator. --- Regularity theorem. --- Renormalization. --- Riemann surface. --- Riemannian manifold. --- Riesz representation theorem. --- Self-adjoint operator. --- Self-adjoint. --- Sign (mathematics). --- Special case. --- Spectral theorem. --- Spectral theory. --- Summation. --- Support (mathematics). --- Symplectic geometry. --- Symplectic manifold. --- Taylor series. --- Theorem. --- Toeplitz operator. --- Trace class. --- Trigonometric polynomial. --- Unit disk. --- Variable (mathematics). --- Equations aux derivees partielles lineaires --- Équations aux dérivées partielles --- Solutions numériques.