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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
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| Princeton, : Princeton University Press, 2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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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 |
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Lax Peter D.
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| Princeton, NJ : , : Princeton University Press, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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