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The hypoelliptic Laplacian and Ray-Singer metrics [[electronic resource] /] / Jean-Michel Bismut, Gilles Lebeau
The hypoelliptic Laplacian and Ray-Singer metrics [[electronic resource] /] / Jean-Michel Bismut, Gilles Lebeau
Autore Bismut Jean-Michel
Edizione [Course Book]
Pubbl/distr/stampa Princeton, : Princeton University Press, 2008
Descrizione fisica 1 online resource (378 p.)
Disciplina 515/.7242
Altri autori (Persone) LebeauGilles
Collana Annals of mathematics studies
Soggetto topico Differential equations, Hypoelliptic
Laplacian operator
Metric spaces
Soggetto non controllato Alexander Grothendieck
Analytic function
Asymptote
Asymptotic expansion
Berezin integral
Bijection
Brownian dynamics
Brownian motion
Chaos theory
Chern class
Classical Wiener space
Clifford algebra
Cohomology
Combination
Commutator
Computation
Connection form
Coordinate system
Cotangent bundle
Covariance matrix
Curvature tensor
Curvature
De Rham cohomology
Derivative
Determinant
Differentiable manifold
Differential operator
Dirac operator
Direct proof
Eigenform
Eigenvalues and eigenvectors
Ellipse
Embedding
Equation
Estimation
Euclidean space
Explicit formula
Explicit formulae (L-function)
Feynman–Kac formula
Fiber bundle
Fokker–Planck equation
Formal power series
Fourier series
Fourier transform
Fredholm determinant
Function space
Girsanov theorem
Ground state
Heat kernel
Hilbert space
Hodge theory
Holomorphic function
Holomorphic vector bundle
Hypoelliptic operator
Integration by parts
Invertible matrix
Logarithm
Malliavin calculus
Martingale (probability theory)
Matrix calculus
Mellin transform
Morse theory
Notation
Parameter
Parametrix
Parity (mathematics)
Polynomial
Principal bundle
Probabilistic method
Projection (linear algebra)
Rectangle
Resolvent set
Ricci curvature
Riemann–Roch theorem
Scientific notation
Self-adjoint operator
Self-adjoint
Sign convention
Smoothness
Sobolev space
Spectral theory
Square root
Stochastic calculus
Stochastic process
Summation
Supertrace
Symmetric space
Tangent space
Taylor series
Theorem
Theory
Torus
Trace class
Translational symmetry
Transversality (mathematics)
Uniform convergence
Variable (mathematics)
Vector bundle
Vector space
Wave equation
ISBN 1-282-45837-X
9786612458378
1-4008-2906-2
Classificazione SK 620
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Frontmatter -- Contents -- Introduction -- Chapter 1. Elliptic Riemann-Roch-Grothendieck and flat vector bundles -- Chapter 2. The hypoelliptic Laplacian on the cotangent bundle -- Chapter 3. Hodge theory, the hypoelliptic Laplacian and its heat kernel -- Chapter 4. Hypoelliptic Laplacians and odd Chern forms -- Chapter 5. The limit as t → +∞ and b → 0 of the superconnection forms -- Chapter 6. Hypoelliptic torsion and the hypoelliptic Ray-Singer metrics -- Chapter 7. The hypoelliptic torsion forms of a vector bundle -- Chapter 8. Hypoelliptic and elliptic torsions: a comparison formula -- Chapter 9. A comparison formula for the Ray-Singer metrics -- Chapter 10. The harmonic forms for b → 0 and the formal Hodge theorem -- Chapter 11. A proof of equation (8.4.6) -- Chapter 12. A proof of equation (8.4.8) -- Chapter 13. A proof of equation (8.4.7) -- Chapter 14. The integration by parts formula -- Chapter 15. The hypoelliptic estimates -- Chapter 16. Harmonic oscillator and the J0 function -- Chapter 17. The limit of A'2φb,±H as b → 0 -- Bibliography -- Subject Index -- Index of Notation
Record Nr. UNINA-9910781084803321
Bismut Jean-Michel  
Princeton, : Princeton University Press, 2008
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Scattering Theory for Automorphic Functions. (AM-87), Volume 87 / / Peter D. Lax, Ralph S. Phillips
Scattering Theory for Automorphic Functions. (AM-87), Volume 87 / / Peter D. Lax, Ralph S. Phillips
Autore Lax Peter D.
Pubbl/distr/stampa Princeton, NJ : , : Princeton University Press, , [2016]
Descrizione fisica 1 online resource (313 pages)
Disciplina 515.9
Collana Annals of Mathematics Studies
Soggetto topico Automorphic functions
Scattering (Mathematics)
Soggetto non controllato Absolute continuity
Algebra
Analytic continuation
Analytic function
Annulus (mathematics)
Asymptotic distribution
Automorphic function
Bilinear form
Boundary (topology)
Boundary value problem
Bounded operator
Calculation
Cauchy sequence
Change of variables
Complex plane
Conjugacy class
Convolution
Cusp neighborhood
Cyclic group
Derivative
Differential equation
Differential operator
Dimension (vector space)
Dimensional analysis
Dirichlet integral
Dirichlet series
Eigenfunction
Eigenvalues and eigenvectors
Eisenstein series
Elliptic operator
Elliptic partial differential equation
Equation
Equivalence class
Even and odd functions
Existential quantification
Explicit formula
Explicit formulae (L-function)
Exponential function
Fourier transform
Function space
Functional analysis
Functional calculus
Fundamental domain
Harmonic analysis
Hilbert space
Hyperbolic partial differential equation
Infinitesimal generator (stochastic processes)
Integral equation
Integration by parts
Invariant subspace
Laplace operator
Laplace transform
Lebesgue measure
Linear differential equation
Linear space (geometry)
Matrix (mathematics)
Maximum principle
Meromorphic function
Modular group
Neumann boundary condition
Norm (mathematics)
Null vector
Number theory
Operator theory
Orthogonal complement
Orthonormal basis
Paley–Wiener theorem
Partial differential equation
Perturbation theory (quantum mechanics)
Perturbation theory
Primitive element (finite field)
Principal component analysis
Projection (linear algebra)
Quadratic form
Removable singularity
Representation theorem
Resolvent set
Riemann hypothesis
Riemann surface
Riemann zeta function
Riesz representation theorem
Scatter matrix
Scattering theory
Schwarz reflection principle
Selberg trace formula
Self-adjoint
Semigroup
Sign (mathematics)
Spectral theory
Subgroup
Subsequence
Summation
Support (mathematics)
Theorem
Trace class
Trace formula
Unitary operator
Wave equation
Weighted arithmetic mean
Winding number
ISBN 1-4008-8156-0
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Frontmatter -- TABLE OF CONTENTS -- PREFACE -- LIST OF SYMBOLS -- §1. INTRODUCTION -- §2. AN ABSTRACT SCATTERING THEORY -- §3. A MODIFIED THEORY FOR SECOND ORDER EQUATIONS WITH AN INDEFINITE ENERGY FORM -- §4. THE LAPLACE-BELTRAMI OPERATOR FOR THE MODULAR GROUP -- §5. THE AUTOMORPHIC WAVE EQUATIONS -- §6. INCOMING AND OUTGOING SUBSPACES FOR THE AUTOMORPHIC WAVE EQUATION -- §7. THE SCATTERING MATRIX FOR THE AUTOMORPHIC WAVE EQUATION -- §8. THE GENERAL CASE -- §9. THE SELBERG TRACE FORMULA -- REFERENCES -- INDEX -- Backmatter
Record Nr. UNINA-9910154746703321
Lax Peter D.  
Princeton, NJ : , : Princeton University Press, , [2016]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Seminar on Singularities of Solutions of Linear Partial Differential Equations. (AM-91), Volume 91 / / Lars Hörmander
Seminar on Singularities of Solutions of Linear Partial Differential Equations. (AM-91), Volume 91 / / Lars Hörmander
Autore Hörmander Lars
Pubbl/distr/stampa Princeton, NJ : , : Princeton University Press, , [2016]
Descrizione fisica 1 online resource (296 pages) : illustrations
Disciplina 515/.353
Collana Annals of Mathematics Studies
Soggetto topico Differential equations, Linear - Numerical solutions
Differential equations, Partial - Numerical solutions
Soggetto non controllato 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)
ISBN 1-4008-8158-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Frontmatter -- Contents -- Preface / Hörmander, Lars -- Spectral Analysis of Singularities / Hörmander, Lars -- Fourier Integral Operators with Complex Phase Functions / Sjöstrand, J. -- Hypoelliptic Operators with Double Characteristics / Menikoff, A. -- Differential Boundary Value Problems of Principal Type / Melrose, R. B. -- Propagation of Singularities for a Class of Operators with Double Characteristics / Hanges, Nicholas -- Subelliptic Operators / Hörmander, Lars -- Lacunas and Transmissions / Monvel, Louis Boutet de -- Some Classical Theorems in Spectral Theory Revisited / Guillemin, Victor -- Szegö's Theorem and a Complete Symbolic Calculus for Pseudo-Differential Operators / Widom, Harold -- Backmatter
Record Nr. UNINA-9910154745903321
Hörmander Lars  
Princeton, NJ : , : Princeton University Press, , [2016]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui