# Selected Works of Eberhard Hopf with Commentaries

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*Cathleen S. Morawetz; James B. Serrin; Yakov G. Sinai*

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.

#### Readership

Graduate students and research mathematicians interested in analysis.

#### Reviews & Endorsements

The value and interest of the book is also highly increased by the commentaries on Hopf's main achievements, written by experts … Most of them are real gems. The book also contains a short curriculum vitae, a complete list of publications and a portrait of Eberhard Hopf. It should be in every mathematical library.

-- Zentralblatt MATH