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Introduction to analysis on graphs / Alexander Grigor'yan

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: University lecture series ; volume 71Publisher: Providence, Rhode Island : American Mathematical Society, [2018]Description: 1 Online-RessourceISBN:
  • 1470448556
  • 9781470448554
Subject(s): Additional physical formats: 147044397X | 9781470443979 | Erscheint auch als: Introduction to analysis on graphs. Druck-Ausgabe Providence, Rhode Island : American Mathematical Society, 2018. viii, 150 SeitenDDC classification:
  • 511/.5
MSC: MSC: *05-02 | 05C81 | 60J10 | 05C25 | 05C50 | 05C63RVK: RVK: SK 890LOC classification:
  • QA166
Online resources: Summary: Cover; Title page; Preface; Chapter 1. The Laplace operator on graphs; 1.1. The notion of a graph; 1.2. Cayley graphs; 1.3. Random walks; 1.4. The Laplace operator; 1.5. The Dirichlet problem; Chapter 2. Spectral properties of the Laplace operator; 2.1. Green's formula; 2.2. Eigenvalues of the Laplace operator; 2.3. Convergence to equilibrium; 2.4. More about the eigenvalues; 2.5. Convergence to equilibrium for bipartite graphs; 2.6. Eigenvalues of ℤ_{ }; 2.7. Products of graphs; 2.8. Eigenvalues and mixing time in ℤ_{ }ⁿ, odd.; 2.9. Eigenvalues and mixing time in a binary cubeSummary: Anybody who has ever read a mathematical text of the author would agree that his way of presenting complex material is nothing short of marvelous. This new book showcases again the author's unique ability of presenting challenging topics in a clear and accessible manner, and of guiding the reader with ease to a deep understanding of the subject. --Matthias Keller, University of Potsdam A central object of this book is the discrete Laplace operator on finite and infinite graphs. The eigenvalues of the discrete Laplace operator have long been used in graph theory as a convenient tool for understPPN: PPN: 1048031543Package identifier: Produktsigel: ZDB-4-NLEBK
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