Collected Works 2002; 396 pp; hardcover Volume: 17 ISBN10: 082182077X ISBN13: 9780821820773 List Price: US$120 Member Price: US$96 Order Code: CWORKS/17
 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 wellknown 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 WienerHopf 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 "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 Table of Contents Part I  E. Hopf  Elementare Bemerkungen über die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus
 J. B. Serrin  Commentary
 E. Hopf  A remark on linear elliptic differential equations of second order
 J. B. Serrin  Commentary
 E. Hopf  Zum analytischen Charakter der Lösungen regulärer zweidimensionaler Variationsprobleme
 H. Weinberger  Commentary
 N. Wiener and E. Hopf  Über eine Klasse singulärer Integralgleichungen
 H. Widom  Commentary
 E. Hopf  Über den funktionalen, insbesondere den analytischen Charakter der Lösungen elliptscher Differentialgleichungen zweiter Ordnung
 H. Weinberger  Commentary
 E. Hopf  Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differentialsystems
 M. Golubitsky and P. H. Rabinowitz  Commentary
 E. Hopf  Repeated branching through loss of stability. An example
 E. Hopf  A mathematical example displaying features of turbulence
 R. Temam  Commentary
 E. Hopf  On S. Bernstein's theorem on surfaces \(z(x,y)\) of nonpositive curvature
 L. Nirenberg  Commentary
 E. Hopf  The partial differential equation \(u_t + uu_x = \mu_{xx}\)
 P. D. Lax  Commentary
 E. Hopf  Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen
 J. B. Serrin  Commentary
 E. D. Conway and E. Hopf  Hamilton's theory and generalized solutions of the HamiltonJacobi equation
 C. S. Morawetz  Commentary
Part II  E. Hopf  Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung
 E. Hopf  Statistik der Lösungen geodätischer Probleme vom unstabilen Typus. II
 Ya. G. Sinai  Commentary
 E. Hopf  Closed surfaces without conjugate points
 Ya. G. Sinai  Commentary
 E. Hopf  Statistical hydromechanics and functional calculus
 Ya. G. Sinai  Commentary
 E. Hopf  On the ergodic theorem for positive linear operators
 D. Ornstein  Commentary
 Acknowledgments
