Author: Agnes BenedekPublisher:
ISBN:
Category :
Languages : en
Pages : 66
Book Description
Remarks on a Theorem of A. Pleijel and Related Topics, I
Author: Agnes BenedekActas
Author: Topics in Spectral Geometry
Author: Michael LevitinPublisher: American Mathematical Society
ISBN: 1470475251
Category : Mathematics
Languages : en
Pages : 346
Book Description
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.
Eigenvalues in Riemannian Geometry
Author: Isaac ChavelPublisher: Academic Press
ISBN: 0080874347
Category : Mathematics
Languages : en
Pages : 379
Book Description
The basic goals of the book are: (i) to introduce the subject to those interested in discovering it, (ii) to coherently present a number of basic techniques and results, currently used in the subject, to those working in it, and (iii) to present some of the results that are attractive in their own right, and which lend themselves to a presentation not overburdened with technical machinery.
Mathematical Reviews
Author: Spectral Geometry
Author: Pierre H. BerardPublisher: Springer
ISBN: 3540409580
Category : Mathematics
Languages : en
Pages : 284
Book Description
Function Spaces, Interpolation Theory and Related Topics
Author: Michael CwikelPublisher: Walter de Gruyter
ISBN: 3110198053
Category : Mathematics
Languages : en
Pages : 473
Book Description
This volume contains 16 refereed research articles on function spaces, interpolation theory and related fields. Topics covered: theory of function spaces, Hankel-type and related operators, analysis on bounded symmetric domains, partial differential equations, Green functions, special functions, homogenization theory, Sobolev embeddings, Coxeter groups, spectral theory and wavelets. The book will be of interest to both researchers and graduate students working in interpolation theory, function spaces and operators, partial differential equations and analysis on bounded symmetric domains.
Edgar Krahn 1894-1961
Author: Ülo LumistePublisher: IOS Press
ISBN: 9789051991680
Category : Geometry, Differential
Languages : en
Pages : 212
Book Description
Spectral Theory and Partial Differential Equations
Author: James V RalstonPublisher: American Mathematical Soc.
ISBN: 1470409895
Category : Mathematics
Languages : en
Pages : 210
Book Description
Contains the proceedings of the Conference on Spectral Theory and Partial Differential Equations, held in honor of James Ralston's 70th Birthday. Papers cover important topics in spectral theory and partial differential equations such as inverse problems, both analytical and algebraic; minimal partitions and Pleijel's Theorem; spectral theory for a model in Quantum Field Theory; and beams on Zoll manifolds.
Author: