01395nam0-2200469---450-99000094537020331620090211124853.088-386-5000-40094537USA010094537(ALEPH)000094537USA01009453720020205d1994----km-y0ITAy01------baitaIT||||||||001yyStatisticaMurray R. Spiegel[traduzione Walter Molon]2. edMilanoMcGraw-Hill libri Italia1994VIII, 504 p.26 cmMatematice e statistica4Seguono : AppendiciStatistics2001Matematice e statistica42001Statistics13671StatisticaEsercizi519.5SPIEGEL,Murray R.1929ITsalbcISBD990000945370203316519.5 SPI 1 (IRA 37 6 A)3417 ECIRA519.5 SPI 1a (IRA 37 6 A)3105 ECIRA00170652IRA 37 6 A3105 ECIRABKECOPATTY9020020205USA01132820020403USA011737PATRY9020040406USA011705RSIAV19020081203USA011449RSIAV29020090211USA011248Statistics13671UNISA04705nam 2200733 a 450 991096980160332120240516081923.097866131638759781283163873128316387X9781400840571140084057010.1515/9781400840571(Au-PeEL)EBL729954(CaPaEBR)ebr10481984(CaONFJC)MIL316387(OCoLC)747411206(DE-B1597)446690(OCoLC)979593679(DE-B1597)9781400840571(PPN)199244537(PPN)187958386(CKB)2550000000040205(FR-PaCSA)88838025(MiAaPQ)EBC729954(FRCYB88838025)88838025(EXLCZ)99255000000004020520110803d2011 uy 0engurznu---uuuuutxtccrHypoelliptic Laplacian and orbital integrals /Jean-Michel BismutCourse BookPrinceton Princeton University Press20111 online resource (320 p.)Annals of mathematics studies ;no. 177Description based upon print version of record.9780691151298 0691151296 9780691151304 069115130X Includes bibliographical references and indexes.Frontmatter --Contents --Acknowledgments --Introduction --Chapter One. Clifford and Heisenberg algebras --Chapter Two. The hypoelliptic Laplacian on X = G/K --Chapter Three. The displacement function and the return map --Chapter Four. Elliptic and hypoelliptic orbital integrals --Chapter Five. Evaluation of supertraces for a model operator --Chapter Six. A formula for semisimple orbital integrals --Chapter Seven. An application to local index theory --Chapter Eight. The case where [k (γ) ; p0] = 0 --Chapter Nine. A proof of the main identity --Chapter Ten. The action functional and the harmonic oscillator --Chapter Eleven. The analysis of the hypoelliptic Laplacian --Chapter Twelve. Rough estimates on the scalar heat kernel --Chapter Thirteen. Refined estimates on the scalar heat kernel for bounded b --Chapter Fourteen. The heat kernel qXb;t for bounded b --Chapter Fifteen. The heat kernel qXb;t for b large --Bibliography --Subject Index --Index of NotationThis book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the tangent bundle, and of the generator of the geodesic flow. In this book, semisimple orbital integrals associated with the heat kernel of the Casimir operator are shown to be invariant under a suitable hypoelliptic deformation, which is constructed using the Dirac operator of Kostant. Their explicit evaluation is obtained by localization on geodesics in the symmetric space, in a formula closely related to the Atiyah-Bott fixed point formulas. Orbital integrals associated with the wave kernel are also computed. Estimates on the hypoelliptic heat kernel play a key role in the proofs, and are obtained by combining analytic, geometric, and probabilistic techniques. Analytic techniques emphasize the wavelike aspects of the hypoelliptic heat kernel, while geometrical considerations are needed to obtain proper control of the hypoelliptic heat kernel, especially in the localization process near the geodesics. Probabilistic techniques are especially relevant, because underlying the hypoelliptic deformation is a deformation of dynamical systems on the symmetric space, which interpolates between Brownian motion and the geodesic flow. The Malliavin calculus is used at critical stages of the proof.Annals of mathematics studies ;no. 177.Differential equations, HypoellipticLaplacian operatorDefinite integralsOrbit methodDifferential equations, Hypoelliptic.Laplacian operator.Definite integrals.Orbit method.515.7242Bismut Jean-Michel44924MiAaPQMiAaPQMiAaPQBOOK9910969801603321Hypoelliptic Laplacian and orbital integrals241722UNINA