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Graduate Studies in Mathematics Ser.: Topics in Spectral Geometry by Michael Levitin, Iosif Polterovich and Dan Mangoubi (2024, Hardcover)
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About this product
Product Identifiers
PublisherAmerican Mathematical Society
ISBN-101470475251
ISBN-139781470475253
eBay Product ID (ePID)15063302816
Product Key Features
Number of Pages325 Pages
LanguageEnglish
Publication NameTopics in Spectral Geometry
Publication Year2024
SubjectGeneral
TypeTextbook
Subject AreaMathematics
AuthorMichael Levitin, Iosif Polterovich, Dan Mangoubi
SeriesGraduate Studies in Mathematics Ser.
FormatHardcover
Dimensions
Item Height0.8 in
Item Weight12.9 Oz
Item Length10 in
Item Width7 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2023-030372
Dewey Edition23/eng/20230927
Series Volume Number237
Dewey Decimal516/.07
Table Of ContentStrings, drums, and the Laplacian The spectral theorems Variational principles and applications Nodal geometry of eigenfunctions Eigenvalue inequalities Heat equation, spectral invariants, and isospectrality The Steklov problem and the Dirichlet-to-Neumann map A short tutorial on numerical spectral geometry Background definitions and notation Image credits Bibliography Index
SynopsisIt is remarkable that various distinct physical phenomena, such as wave propagation, heat diffusion, electron movement in quantum mechanics, oscillations of fluid in a container, can be described using the same differential operator, the Laplacian. Spectral data (i.e., eigenvalues and eigenfunctions) of the Laplacian depend in a subtle way on the geometry of the underlying object, e.g., a Euclidean domain or a Riemannian manifold, on which the operator is defined. This dependence, or, rather, the interplay between the geometry and the spectrum, is the main subject of spectral geometry. Its roots can be traced to Ernst Chladni's experiments with vibrating plates, Lord Rayleigh's theory of sound, and Mark Kac's celebrated question ""Can one hear the shape of a drum?"" In the second half of the twentieth century spectral geometry emerged as a separate branch of geometric analysis. Nowadays it is a rapidly developing area of mathematics, with close connections to other fields, such as differential geometry, mathematical physics, partial differential equations, number theory, dynamical systems, and numerical analysis. This book can be used for a graduate or an advanced undergraduate course on spectral geometry, starting from the basics but at the same time covering some of the exciting recent developments which can be explained without too many prerequisites., It is remarkable that various distinct physical phenomena, such as wave propagation, heat diffusion, electron movement in quantum mechanics, oscillations of fluid in a container, can be described using the same differential operator, the Laplacian. Spectral data (i.e., eigenvalues and eigenfunctions) of the Laplacian depend in a subtle way on the ......
LC Classification NumberQA614.95.L48 2023
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