TY  - GEN
T1  - The hypoelliptic Laplacian and Ray-Singer metrics
T2  - Annals of mathematics studies ;
A1  - Bismut, Jean-Michel
A2  - Lebeau, Gilles
LA  - English
PP  - Princeton
PB  - Princeton University Press
YR  - 2008
UL  - https://ebooks.jgu.edu.in/Record/ebsco_acadsubs_ocn593214464
AB  - This book presents the analytic foundations to the theory of the hypoelliptic Laplacian. The hypoelliptic Laplacian, a second-order operator acting on the cotangent bundle of a compact manifold, is supposed to interpolate between the classical Laplacian and the geodesic flow. Jean-Michel Bismut and Gilles Lebeau establish the basic functional analytic properties of this operator, which is also studied from the perspective of local index theory and analytic torsion. The book shows that the hypoelliptic Laplacian provides a geometric version of the Fokker-Planck equations. The authors give th.
OP  - 367
CN  - QA377 .B674 2008eb
SN  - 9781400829064
SN  - 1400829062
SN  - 9786612458378
SN  - 6612458372
SN  - 9781282458376
SN  - 128245837X
SN  - 9780691137315
SN  - 0691137315
SN  - 9780691137322
SN  - 0691137323
KW  - Differential equations, Hypoelliptic.
KW  - Laplacian operator.
KW  - Metric spaces.
KW  - Équations différentielles hypo-elliptiques.
KW  - Laplacien.
KW  - Espaces métriques.
KW  - MATHEMATICS : Functional Analysis.
KW  - MATHEMATICS : Geometry : General.
KW  - Differential equations, Hypoelliptic
KW  - Laplacian operator
KW  - Metric spaces
KW  - Hodge-Theorie
KW  - Hypoelliptischer Operator
KW  - Laplace-Operator
KW  - Elliptische differentiaalvergelijkingen.
KW  - Laplace-operatoren.
KW  - Metrische ruimten.
KW  - Partiële differentiaalvergelijkingen.
KW  - Tweede orde.
KW  - Alexander Grothendieck.
KW  - Analytic function.
KW  - Asymptote.
KW  - Asymptotic expansion.
KW  - Berezin integral.
KW  - Bijection.
KW  - Brownian dynamics.
KW  - Brownian motion.
KW  - Chaos theory.
KW  - Chern class.
KW  - Classical Wiener space.
KW  - Clifford algebra.
KW  - Cohomology.
KW  - Combination.
KW  - Commutator.
KW  - Computation.
KW  - Connection form.
KW  - Coordinate system.
KW  - Cotangent bundle.
KW  - Covariance matrix.
KW  - Curvature tensor.
KW  - Curvature.
KW  - De Rham cohomology.
KW  - Derivative.
KW  - Determinant.
KW  - Differentiable manifold.
KW  - Differential operator.
KW  - Dirac operator.
KW  - Direct proof.
KW  - Eigenform.
KW  - Eigenvalues and eigenvectors.
KW  - Ellipse.
KW  - Embedding.
KW  - Equation.
KW  - Estimation.
KW  - Euclidean space.
KW  - Explicit formula.
KW  - Explicit formulae (L-function).
KW  - Feynman-Kac formula.
KW  - Fiber bundle.
KW  - Fokker-Planck equation.
KW  - Formal power series.
KW  - Fourier series.
KW  - Fourier transform.
KW  - Fredholm determinant.
KW  - Function space.
KW  - Girsanov theorem.
KW  - Ground state.
KW  - Heat kernel.
KW  - Hilbert space.
KW  - Hodge theory.
KW  - Holomorphic function.
KW  - Holomorphic vector bundle.
KW  - Hypoelliptic operator.
KW  - Integration by parts.
KW  - Invertible matrix.
KW  - Logarithm.
KW  - Malliavin calculus.
KW  - Martingale (probability theory).
KW  - Matrix calculus.
KW  - Mellin transform.
KW  - Morse theory.
KW  - Notation.
KW  - Parameter.
KW  - Parametrix.
KW  - Parity (mathematics).
KW  - Polynomial.
KW  - Principal bundle.
KW  - Probabilistic method.
KW  - Projection (linear algebra).
KW  - Rectangle.
KW  - Resolvent set.
KW  - Ricci curvature.
KW  - Riemann-Roch theorem.
KW  - Scientific notation.
KW  - Self-adjoint operator.
KW  - Self-adjoint.
KW  - Sign convention.
KW  - Smoothness.
KW  - Sobolev space.
KW  - Spectral theory.
KW  - Square root.
KW  - Stochastic calculus.
KW  - Stochastic process.
KW  - Summation.
KW  - Supertrace.
KW  - Symmetric space.
KW  - Tangent space.
KW  - Taylor series.
KW  - Theorem.
KW  - Theory.
KW  - Torus.
KW  - Trace class.
KW  - Translational symmetry.
KW  - Transversality (mathematics).
KW  - Uniform convergence.
KW  - Variable (mathematics).
KW  - Vector bundle.
KW  - Vector space.
KW  - Wave equation.
ER  -