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Selected Works of Eberhard Hopf with Commentaries
Eberhard Hopf
其他書名
With Commentaries
出版American Mathematical Soc., 2002
主題Mathematics / CalculusMathematics / Linear & Nonlinear ProgrammingMathematics / TransformationsMathematics / Mathematical AnalysisMathematics / Complex AnalysisScience / Mechanics / Fluids
ISBN082182077X9780821820773
URLhttp://books.google.com.hk/books?id=8TOqgRLbpaQC&hl=&source=gbs_api
EBookSAMPLE
註釋This work celebrates the work of Eberhard Hopf, a founding father of ergodic theory, a mathematician who produced many beautiful, elegantly written, and now classical results in integral equations and partial differential equations. Hopf's results remain at the core of these fields, and the title includes Hopf's original mathematical papers, still notable for their elegance and clarity of the writing, with accompanying summaries and commentary by well-known mathematicians. Today, ergodic theory and P.D.E. continue to be active, important areas of mathematics. In this volume the reader will find the roots of many ergodic theory concepts and theorems. Hopf authored fundamental results for P.D.E., such as the maximum principle of elliptic equations and the complete solution of Burger's equation. The familiar properties of elliptic equations were proved for the first time in his earliest work and are included here. His bifurcation theorem, still used over and over again, is a particular gem. The proof of the Wiener-Hopf Theorem is a stunning application of deep analysis. The volume is presented in two main parts. The first section is dedicated to classical papers in analysis and fluid dynamics, and the second to ergodic theory. These works and all the others in the Selected Works carry commentaries by a stellar group of mathematicians who write of the origin of the problems, the important results that followed. Many a mathematical researcher and graduate student will find these collected works to be an excellent resource.