Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) By: Christopher D. Sogge Publisher: Princeton University Press Print ISBN: 9780691160757, 0691160759 eText ISBN: 9781400850549, 1400850541 Pages: 208 Copyright year: 2014 Format: PDF Available from $ 82.50 USD SKU 9781400850549 Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. Christopher Sogge gives a proof of the sharp Weyl formula for the distribution of eigenvalues of Laplace-Beltrami operators, as well as an improved version of the Weyl formula, the Duistermaat-Guillemin theorem under natural assumptions on the geodesic flow. Sogge shows that there is quantum ergodicity of eigenfunctions if the geodesic flow is ergodic. Sogge begins with a treatment of the Hadamard parametrix before proving the first main result, the sharp Weyl formula. He avoids the use of Tauberian estimates and instead relies on sup-norm estimates for eigenfunctions. The author also gives a rapid introduction to the stationary phase and the basics of the theory of pseudodifferential operators and microlocal analysis. These are used to prove the Duistermaat-Guillemin theorem. Turning to the related topic of quantum ergodicity, Sogge demonstrates that if the long-term geodesic flow is uniformly distributed, most eigenfunctions exhibit a similar behavior, in the sense that their mass becomes equidistributed as their frequencies go to infinity. Additional ISBNs 9780691160788, 9780691160757, 0691160783, 0691160759, 9780691160788, 0691160783 Ebooks here: https://ouo.io/D0wO23
