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...

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Hauptverfasser:	Levitin, Michael 1963- (VerfasserIn), Mangoubi, Dan 1974- (VerfasserIn), Polterovich, Iosif 1974- (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Providence, Rhode Island American Mathematical Society [2023]
Schriftenreihe:	Graduate studies in mathematics Volume 237
Schlagworte:	Spectral geometry Eigenfunctions Operator theory > General theory of linear operators > Eigenvalue problems Global analysis, analysis on manifolds > Calculus on manifolds; nonlinear operators > Spectral theory; eigenvalue problems Global analysis, analysis on manifolds > Partial differential equations on manifolds; differential operators > Spectral problems; spectral geometry; scattering theory Global analysis, analysis on manifolds > Partial differential equations on manifolds; differential operators > Isospectrality Numerical analysis > Partial differential equations, boundary value problems > Eigenvalue problems
Online-Zugang:	Volltext
Zusammenfassung:	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 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 Chladnis experiments with vibrating plates, Lord Rayleighs theory of sound, and Mark Kacs 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.
Beschreibung:	Literaturverzeichnis: Seite 297-320 und Index
Beschreibung:	1 Online-Ressource (xviii, 325 Seiten) Illustrationen, Diagramme
ISBN:	9781470475499 9781470475253
DOI:	10.1090/gsm/237