Introduction to Isospectrality / by Alberto Arabia

By:

Arabia, Alberto [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Universitext | Springer eBook CollectionPublisher: Cham : Springer International Publishing, 2022Publisher: Cham : Imprint: Springer, 2022Edition: 1st ed. 2022Description: 1 Online-Ressource(XI, 238 p. 154 illus., 142 illus. in color.)ISBN:

9783031171239

Subject(s):

Additional physical formats: 9783031171222 | 9783031171246 | Erscheint auch als: 9783031171222 Druck-Ausgabe | Erscheint auch als: 9783031171246 Druck-Ausgabe | Erscheint auch als: Introduction to isospectrality. Druck-Ausgabe Cham : Springer, 2022. xi, 238 SeitenDOI: DOI: 10.1007/978-3-031-17123-9Online resources:

Summary: 1 Introduction -- 2 The Wave Equation on Flat Manifolds -- 3 The Sunada–Bérard–Buser Method -- 4 The Gordon–Webb–Wolpert Isospectral Domains -- A Linear Representations of Finite Groups and Almost-Conjugate Subgroups -- B The Laplacian as Isometry-Invariant Differential Operator -- C The Path-Distance on a Hausdorff Connected Flat Manifold -- D Group Quotients of Flat Manifolds -- References -- Glossary -- Index.Summary: "Can one hear the shape of a drum?" This striking question, made famous by Mark Kac, conceals a precise mathematical problem, whose study led to sophisticated mathematics. This textbook presents the theory underlying the problem, for the first time in a form accessible to students. Specifically, this book provides a detailed presentation of Sunada's method and the construction of non-isometric yet isospectral drum membranes, as first discovered by Gordon–Webb–Wolpert. The book begins with an introductory chapter on Spectral Geometry, emphasizing isospectrality and providing a panoramic view (without proofs) of the Sunada–Bérard–Buser strategy. The rest of the book consists of three chapters. Chapter 2 gives an elementary treatment of flat surfaces and describes Buser's combinatorial method to construct a flat surface with a given group of isometries (a Buser surface). Chapter 3 proves the main isospectrality theorems and describes the transplantation technique on Buser surfaces. Chapter 4 builds Gordon–Webb–Wolpert domains from Buser surfaces and establishes their isospectrality. Richly illustrated and supported by four substantial appendices, this book is suitable for lecture courses to students having completed introductory graduate courses in algebra, analysis, differential geometry and topology. It also offers researchers an elegant, self-contained reference on the topic of isospectrality.PPN: PPN: 1816990183Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS

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