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[null,"1.","Record Nr.",null,"UNISA996386814203316"]
[null,null,"Titolo",null,"A Touch of the times, or, Two letters casually intercepted [[electronic resource] ] : the first, from the author of a late pamplet intituled, Day-fatality, to the supposed author of the Weekly packet of advice from Rome, 1679 : the second, the answer thereunto"]
[null,null,"Pubbl/distr/stampa",null,"[London, : s.n., 1679]"]
[null,null,"Descrizione fisica",null,"1 sheet (2 p.)"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Caption title."]
[{"$nulls":4},"Place and date of publication suggested by Wing."]
[{"$nulls":4},"Reproduction of original in the Harvard University Library."]
[null,null,null,"Sommario/riassunto","eebo-0062"]
[null,"2.","Record Nr.",null,"UNINA9910969801603321"]
[null,null,"Autore",null,"Bismut Jean-Michel"]
[null,null,"Titolo",null,"Hypoelliptic Laplacian and orbital integrals / / Jean-Michel Bismut"]
[null,null,"Pubbl/distr/stampa",null,"Princeton, : Princeton University Press, 2011"]
[null,null,"ISBN",null,"9786613163875"]
[{"$nulls":4},"9781283163873"]
[{"$nulls":4},"128316387X"]
[{"$nulls":4},"9781400840571"]
[{"$nulls":4},"1400840570"]
[null,null,"Edizione",null,"[Course Book]"]
[null,null,"Descrizione fisica",null,"1 online resource (320 p.)"]
[null,null,"Collana",null,"Annals of mathematics studies ; ; no. 177"]
[null,null,"Disciplina",null,"515.7242"]
[null,null,"Soggetti",null,"Differential equations, Hypoelliptic"]
[{"$nulls":4},"Laplacian operator"]
[{"$nulls":4},"Definite integrals"]
[{"$nulls":4},"Orbit method"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and indexes."]
[null,null,"Nota di contenuto",null,"Frontmatter -- Contents -- Acknowledgments -- Introduction -- Chapter One. Clifford and Heisenberg algebras -- Chapter Two. The hypoelliptic Laplacian on X = G/K -- Chapter Three. The displacement function and the return map -- Chapter Four. Elliptic and hypoelliptic orbital integrals -- Chapter Five. Evaluation of supertraces for a model operator -- Chapter Six. A formula for semisimple orbital integrals -- Chapter Seven. An application to local index theory -- Chapter Eight. The case where [k (γ) ; p0] = 0 -- Chapter Nine. A proof of the main identity -- Chapter Ten. The action functional and the harmonic oscillator -- Chapter Eleven. The analysis of the hypoelliptic Laplacian -- Chapter Twelve. Rough estimates on the scalar heat kernel -- Chapter Thirteen. Refined estimates on the scalar heat kernel for bounded b -- Chapter Fourteen. The heat kernel qXb;t for bounded b -- Chapter Fifteen. The heat kernel qXb;t for b large -- Bibliography -- Subject Index -- Index of Notation"]
[null,null,null,"Sommario/riassunto","This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is "]
[{"$nulls":4},"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."]