Selected Works of Eberhard Hopf with Commentaries: With CommentariesAmerican Mathematical Soc., 2002 - 396 pàgines 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. |
Continguts
Commentary by James B Serrin | 9 |
A Remark on Linear Elliptic Differential Equations of Second Order | 15 |
Zum analytischen Charakter der Lösungen regulärer zweidimensionaler | 21 |
Commentary by Hans Weinberger | 31 |
Commentary by Harold Widom | 47 |
Lösungen 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 Lösungen geodätischer Probleme vom unstabilen Typus II | 317 |
Commentaries by Ya G Sinai | 337 |
On the Ergodic Theorem for Positive Linear Operators | 387 |
A mathematical example displaying features of turbulence | 127 |
Frases i termes més freqüents
Ableitungen analytisch asymptotisch Behauptung beiden beliebig Bereiche beschränkt Beweis beweisen bewiesen bifurcation boundary daher defined definiert die Lösung differential equations Differentialgleichung dx dt Eberhard Hopf Eigenschaften einmal elliptischen endlich erfüllt ergibt ergodic theory erste ersten Exponenten Feld festen Flächen fluid Folge folgende folgenden folgt follows function Funktionen für Gebiete genügen genügt geodätische Strömung Geodätischen gibt gilt gleich gleichmäßig Gleichung Gleichungen Halbstrahlen Hamilton-Jacobi equation Hopf Hopf theorem Hopf's inequality initial value problem initial values Integral jedem Klasse konst konstant längs leicht Lemma linear Linienelemente Lipschitz continuous Lösung Lösungen Math maximum principle Menge muß Navier-Stokes equations Null obigen positiv problem proof Punkte Raum regulär Richtung satisfies Satz seien Sinne somit Stelle stetig differenzierbar t₁ t₂ theorem überall unendlich Ungleichung Voraussetzung weak solution wieder Winkel x₁ y₁ zunächst zwei zweiten ди