Selected Works of Eberhard Hopf: With Commentaries

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American Mathematical Soc., 2002 - Mathematics - 396 pages
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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.
  

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Contents

Commentary by James B Serrin
9
A Remark on Linear Elliptic Differential Equations of Second Order
15
Zum analytischen Charakter der Losungen regularer zweidimensionaler
21
Commentary by Hans Weinberger
31
Commentary by Harold Widom
47
Losungen elliptischer Differentialgleichungen zweiter Ordnung
49
Commentary by Hans Weinberger
89
Commentary by Martin Golubitsky and Paul H Rabinowitz
111
Commentaries by Roger Temam
147
Commentary by Peter Lax
189
Commentary by James B Serrin
213
Commentary by Cathleen S Morawetz
269
Statistik der Losungen geodatischer Probleme vom unstabilen Typus II
317
Commentaries by Ya G Sinai
337
On the Ergodic Theorem for Positive Linear Operators
387
Copyright

A mathematical example displaying features of turbulence
127

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