Topics in spectral geometry:
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...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
AMS, American Mathematical Society
[2023]
|
| Schriftenreihe: | Graduate studies in mathematics
237 |
| Schlagworte: |
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
|
| 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 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. |
| Beschreibung: | Literaturverzeichnis: Seite 297-320 und Index |
| Beschreibung: | xviii, 325 Seiten Illustrationen, Diagramme |
| ISBN: | 9781470475253 9781470475482 |
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| 490 | 1 | |a Graduate studies in mathematics |v 237 | |
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| 520 | 3 | |a 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 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. | |
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| 653 | 0 | |a Global analysis, analysis on manifolds -- Calculus on manifolds; nonlinear operators -- Spectral theory; eigenvalue problems | |
| 653 | 0 | |a Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Spectral problems; spectral geometry; scattering theory | |
| 653 | 0 | |a Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Isospectrality | |
| 653 | 0 | |a Numerical analysis -- Partial differential equations, boundary value problems -- Eigenvalue problems | |
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| discipline | Mathematik |
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| id | DE-604.BV049646592 |
| illustrated | Illustrated |
| index_date | 2024-07-03T23:39:55Z |
| indexdate | 2025-01-29T17:03:17Z |
| institution | BVB |
| isbn | 9781470475253 9781470475482 |
| language | English |
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| physical | xviii, 325 Seiten Illustrationen, Diagramme |
| publishDate | 2023 |
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| spelling | Levitin, Michael 1963- Verfasser (DE-588)143226142 aut Topics in spectral geometry Michael Levitin, Dan Mangoubi, Iosif Polterovich Providence, Rhode Island AMS, American Mathematical Society [2023] © 2023 xviii, 325 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 237 Literaturverzeichnis: Seite 297-320 und Index 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 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. Spektralgeometrie (DE-588)4128531-1 gnd rswk-swf 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 Spektralgeometrie (DE-588)4128531-1 s DE-604 Mangoubi, Dan 1974- Verfasser (DE-588)1318190975 aut Polterovich, Iosif 1974- Verfasser (DE-588)1156758416 aut Erscheint auch als Online-Ausgabe 978-1-4704-7549-9 ebook Graduate studies in mathematics 237 (DE-604)BV009739289 237 |
| spellingShingle | Levitin, Michael 1963- Mangoubi, Dan 1974- Polterovich, Iosif 1974- Topics in spectral geometry Graduate studies in mathematics Spektralgeometrie (DE-588)4128531-1 gnd |
| subject_GND | (DE-588)4128531-1 |
| title | Topics in spectral geometry |
| title_auth | Topics in spectral geometry |
| title_exact_search | Topics in spectral geometry |
| title_exact_search_txtP | Topics in spectral geometry |
| title_full | Topics in spectral geometry Michael Levitin, Dan Mangoubi, Iosif Polterovich |
| title_fullStr | Topics in spectral geometry Michael Levitin, Dan Mangoubi, Iosif Polterovich |
| title_full_unstemmed | Topics in spectral geometry Michael Levitin, Dan Mangoubi, Iosif Polterovich |
| title_short | Topics in spectral geometry |
| title_sort | topics in spectral geometry |
| topic | Spektralgeometrie (DE-588)4128531-1 gnd |
| topic_facet | Spektralgeometrie |
| volume_link | (DE-604)BV009739289 |
| work_keys_str_mv | AT levitinmichael topicsinspectralgeometry AT mangoubidan topicsinspectralgeometry AT polterovichiosif topicsinspectralgeometry |