Collected papers. Volumes 1,2. Ed. by Jürgen Moser
type: Item
instance of: scholarly article
title: Collected papers. Volumes 1,2. Ed. by Jürgen Moser
zbMATH Open document ID: 0584.01025
author: Fritz John
published in: Contemporary Mathematicians
publication date: 1985-01-01T00:00:00Z
review text: Fritz John was born in Berlin in 1910, obtained his Ph. D. from the University of Göttingen in the ominous year 1933; he left Germany in 1934 for Great Britain and later the USA. The papers collected in these two volumes cover the period 1934-1984 and they have been arranged by subject. There are the following sections: I) Random Transfer, II) Differential Equations; III) Ill-posed problems; IV) Formation of Singularities, V) Numerical Methods, VI) Elasticity Theory; VII) Water Waves, VIII) Geometric Inequalities and Convexity; IX) Functions of Bounded Mean Oscillations; X) Miscellaneous. The editor, J. Moser, starts his preface with the following appreciation: ''The mathematical works of Fritz John whose deep and original ideas have had a great influence on the development of various fields in mathematical analysis are made available with these volumes. His works are certainly well known to the experts, but knowledge of his contributions may not have spread as widely as it should have. For example, the concept of functions of bounded mean oscillations plays a central role in harmonic analysis today, but it is perhaps less known that this class of functions was introduced by John as early as 1961, motivated by his work in elasticity theory. With the publication of this collection, a wider circle of mathematicians will become familiar with, and appreciate, the fertile ideas of Fritz John''. The editing has been done with great care. There is a personal foreword by Gårding, a list of publications of John, a biographical sketch; moreover most sections end with remarks by the author and comments by a number of distinguished mathematicians. We mention some examples. In section II we find a paper on algebraic conditions for hyperbolicity of systems of partial differential equations, which according to P. D. Lax, represents 'a very original contribution to algebraic geometry over \({\mathbb{R}}'\). To the disappointment of many applied mathematicians, this has been a subje…
Mathematics Subject Classification ID: 01A75
Mathematics Subject Classification ID: 35-03
Mathematics Subject Classification ID: 74-03
zbMATH DE Number: 3934994
zbMATH Keywords: Random Transfer
zbMATH Keywords: Differential Equations
zbMATH Keywords: Numerical Methods
zbMATH Keywords: Elasticity Theory
zbMATH Keywords: Water Waves
zbMATH Keywords: Geometric Inequalities and Convexity
zbMATH Keywords: Bounded Mean Oscillations
zbMATH Keywords: harmonic analysis
reviewed by: Ferdinand Verhulst
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3934994