( 0 customer ratings)
Princeton University Press, August 2011
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 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.
$40.29 List price: $65.00 You save: 38% ($24.71)
If you use one of Kobo's free reading apps you won't need to worry about download options most of the time. Your Kobo reading app can easily add Kobo Store books to your library for a seamless reading experience.
Download options matter when:
In both of these cases you will need to:
You can also use Digital Editions to transfer the book to your eReader. See here for more information on Digital Editions.
You can read this item on your computer using our free Kobo Desktop Application. This application lets you read, manage your library of eBooks, and even shop for new ones. Check out our demo for more information!
Learn More »You can read this item on your Kobo eReader (or other select electronic reading devices). The Kobo eReader lets you carry your whole library with you, so that you can read on the go.
Visit kobo.com/ereaders »You can read this item on select tablets using one of our free Kobo apps. These apps let you read, manage your library of eBooks, and even shop for new ones.
Learn More »You can read this item on your Kobo Vox eReader. The Kobo Vox eReader lets you read books with color, sound or interactive elements. Check out our demo for more information on the Kobo Vox.
Learn More »You can read this item on your Kobo Arc using the Library app. This app lets you read, manage your library of eBooks, and shop for new books.
Learn More »You can read this item on any Android device (phone, tablet) with one of our free Kobo apps. These apps let you read, manage your library of eBooks, and even shop for new ones.
Learn More »You can read this item on the free Kobo app for iPhone. This app let you read, manage your library of eBooks, and even shop for new ones.
Download the iPhone App! Learn More »
By: {2}
Available on: {3}
Coming soon
Secure TransactionSubtotal
Store Credit
Total
We'll charge your credit card {4} on {3}.
We'll charge your credit card {4} when the book is added to your Library.
Your store credit covers the cost of this purchase, so we don't charge your credit card
Use Quick Buy for all eBook purchases.{2} is now in your library. You'll receive an email confirming your purchase very soon.
{2} has been pre-ordered. You'll receive a confirmation email confirming your pre-order very soon.
You were charged:
You will be charged: on {3}
You will be charged: when the book is added to your Library
Rakuten Super Points earned: {1}
Rakuten Super Points {1} earned after the book is added to your Library
