ComplexAnalysis:TheGeometricViewpoint,SecondEdition(CarusMathematicalMonographs)

ComplexAnalysis:TheGeometricViewpoint,SecondEdition(CarusMathematicalMonographs)

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作者: Steven G. Krantz 著

出版社: TheMathematicalAssociaitonofAmerica

出版时间: 2004-01

版次: 2

ISBN: 9780883850350

定价: 429.90

装帧: 精装

页数: 234页

正文语种: 英语

分类: 外文古旧书>英文书>自然科学

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Current research on the spectral theory of finite graphs may be seen as part of a wider effort to forge closer links between algebra and combinatorics (in particular between linear algebra and graph theory).This book describes how this topic can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labelling of graph vertices, using geometrical invariants of eigenspaces such as graph angles and main angles, and introducing certain kinds of canonical eigenvectors by means of star partitions and star bases. One objective is to describe graphs by algebraic means as far as possible, and the book discusses the Ulam reconstruction conjecture and the graph isomorphism problem in this context. Further problems of graph reconstruction and identification are used to illustrate the importance of graph angles and star partitions in relation to graph structure. Specialists in graph theory will welcome this treatment of important new research. Steven G. Krantz, currently Professor and Chairman of Mathematics at Washington University in St. Louis, earned hid PhD at Princeton University and has taught at UCLA, Princeton University and Pennsylvania State University. He is the recipient of the UCLA Alumni Foundation Distinguished Teaching Award, the MAA’s Chauvenet Prize, the MAA Beckenbach Book Award, and the Outstanding Academic Book Award of the Current Review of Academic Libraries. He has written numerous books including: "Function Theory of Several Complex Variables," "Real Analysis and Foundations, The Geometry of Domains in Space" (with Harold R. Parks)," Function Theory of One Complex Variable" (with Robert E. Greene), "The Implicit Function Theorem "(with Harold Parks and "A Panorama of Harmonic Analysis" and "Mathematical Apocrypha" (for the MAA). He is also the author of over one-hundred research articles.
内容简介:
Current research on the spectral theory of finite graphs may be seen as part of a wider effort to forge closer links between algebra and combinatorics (in particular between linear algebra and graph theory).This book describes how this topic can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labelling of graph vertices, using geometrical invariants of eigenspaces such as graph angles and main angles, and introducing certain kinds of canonical eigenvectors by means of star partitions and star bases. One objective is to describe graphs by algebraic means as far as possible, and the book discusses the Ulam reconstruction conjecture and the graph isomorphism problem in this context. Further problems of graph reconstruction and identification are used to illustrate the importance of graph angles and star partitions in relation to graph structure. Specialists in graph theory will welcome this treatment of important new research.
作者简介:
Steven G. Krantz, currently Professor and Chairman of Mathematics at Washington University in St. Louis, earned hid PhD at Princeton University and has taught at UCLA, Princeton University and Pennsylvania State University. He is the recipient of the UCLA Alumni Foundation Distinguished Teaching Award, the MAA’s Chauvenet Prize, the MAA Beckenbach Book Award, and the Outstanding Academic Book Award of the Current Review of Academic Libraries. He has written numerous books including: "Function Theory of Several Complex Variables," "Real Analysis and Foundations, The Geometry of Domains in Space" (with Harold R. Parks)," Function Theory of One Complex Variable" (with Robert E. Greene), "The Implicit Function Theorem "(with Harold Parks and "A Panorama of Harmonic Analysis" and "Mathematical Apocrypha" (for the MAA). He is also the author of over one-hundred research articles.

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