{"product_id":"hangzhou-lectures-on-eigenfunctions-of-christopher-d-sogge-9780691160788","title":"Hangzhou Lectures on Eigenfunctions of the Laplacian","description":"\u003cp\u003eBased 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. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eSogge 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Christopher D. Sogge\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0691160783\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780691160788\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Princeton University Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 03\/10\/2014\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 208\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.97lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.93h x 7.13w x 0.54d","brand":"Christopher D. Sogge","offers":[{"title":"Paperback","offer_id":44076221661439,"sku":"9780691160788","price":92.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_999b67ce-e933-49cf-a0d6-242fcb32018b.jpg?v=1685463832","url":"https:\/\/www.whiterainbookhouse.com\/products\/hangzhou-lectures-on-eigenfunctions-of-christopher-d-sogge-9780691160788","provider":"WR Book House","version":"1.0","type":"link"}