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Fritz John, 1910–1994 an Elegant Construction of the Fundamental Solution for Par- Fritz John Died in New Rochelle, NY, on February 10, 1994 people.qxp 3/16/99 5:26 PM Page 255 Mathematics People Mathematics of the AMS and the Society for Industrial and Moser Receives Wolf Prize Applied Mathematics (1968), the Craig Watson Medal of Jürgen Moser of the Eidgenössische Technische Hochschule the U.S. National Academy of Sciences (1969), the John von in Zürich will receive the 1994–1995 Wolf Prize in Mathe- Neumann Lectureship of SIAM (1984), the L. E. J. Brouwer matics. The noted German mathematician will be honored Medal (1984), an Honorary Professorship at the Instituto with the $100,000 award by the Israel-based Wolf Foun- de Matematica Pura e Applicada (1989), and an honorary dation for his “fundamental work on stability in Hamil- doctorate from the University of Bochum (1990). Moser is tonian mechanics and his profound and influential con- a member of the U.S. National Academy of Sciences. tributions to nonlinear differential equations.” The 1994–1995 Wolf Prizes will be presented in March —from Wolf Foundation News Release by the president of Israel, Ezer Weizman, at the Knesset (Parliament) building in Jerusalem. A total of $600,000 will be awarded for outstanding achievements in the fields Aisenstadt Prizes Announced of agriculture, chemistry, physics, medicine, the arts, and mathematics. The Wolf Foundation was established by the The Centre de Recherches Mathématiques in Montreal has late Ricardo Wolf, an inventor, diplomat, and philanthropist. announced that the third and fourth André Aisenstadt Among Moser’s most important achievements is his Mathematics Prizes have been awarded to Nigel D. Hig- role in the development of KAM (Kolmogorov-Arnold- son of Pennsylvania State University and Michael J. Ward Moser) theory, which describes the structure and stability of the University of British Columbia. of dynamical systems which are close to being completely Higson was cited for his contributions to operator integrable. It has shaped the modern theory of Hamilton- algebras, particularly the algebraic K-theory of C∗- ian mechanics and has wide applications in science. algebras. He is responsible for important developments Moser is also known for his proof of the so-called Har- in Kasparov’s KK-theory and in the index theory for op- nack inequality in elliptic and parabolic differential equa- erator algebras. Higson received his B.S. and M.Sc. from tions, which has become a standard tool in nonlinear par- Dalhousie University in Halifax, Nova Scotia. In 1986 he tial differential equations. In addition, he did fundamental received his Ph.D., under the direction of P. A. Fillmore, work in analysis related to complex, symplectic, and dif- from that same institution. Higson then went to the Uni- ferential geometry, in particular the classification of local versity of Pennsylvania and in 1990 moved to Pennsylva- invariants of complex manifolds, nonlinear Sobolev in- nia State University, where he is currently an associate pro- equalities, deformation techniques for symplectic struc- fessor. He held a Sloan Foundation Research Fellowship tures, and stability of foliations. (1992–1994). Moser was born in 1928 in Königsberg, Germany. He re- Michael Ward was recognized for his work in asymp- ceived his doctorate in 1952 from the University of Göt- totics, scientific computing, and mathematical modeling tingen. The following year he was a Fulbright Fellow at New with emphasis on modern applications of physical ap- York University and after that became an assistant professor plied mathematics. His research has applications to semi- there. He was an associate professor at the Massachusetts conductor device modeling, steady-state combustion the- Institute of Technology (1957–1960) and a professor at the ory, diffusion in singularly perturbed domains, reaction Courant Institute of Mathematical Sciences (1960–1980). diffusion models exhibiting interfacial dynamics and From 1967 to 1970 he served as the director of Courant. metastable behavior, and strong localized inhomogeneities Since 1980 he has been a professor at ETH–Zürich, where in various physical systems. Ward received his B.Sc. in he has served as director of the mathematics research in- mathematics from the University of British Columbia and stitute since 1984. his Ph.D. in applied mathematics in 1988 from the Cali- Moser served as the president of the International Math- fornia Institute of Technology, under the direction of Don- ematical Union from 1983 to 1986. Among his awards and ald S. Cohen. After stays at Stanford University and the honors are the George David Birkhoff Prize in Applied Courant Institute for Mathematical Sciences, he returned FEBRUARY 1995 NOTICES OF THE AMS 255 people.qxp 3/16/99 5:26 PM Page 256 Mathematics People in 1992 to the University of British Columbia, where he is originality of John’s work. For him the separation of pure currently an assistant professor. and applied mathematics was meaningless. In fact, his The Aisenstadt Prize of $3,000, named for the philan- work exemplifies the unity of mathematics as well as its thropist André Aisenstadt, is intended to recognize and re- elegance and beauty. This is not the place to discuss in any ward talented young Canadian mathematicians. The win- detail F. John’s work, which is largely accessible in his Col- ners were selected by a CRM steering committee of lected works. Let me illustrate John’s mastery in handling distinguished mathematicians. interconnections between pure and applied problems by several examples. —from CRM News Release The first is John’s work on the Radon transform, which was the theme of his dissertation. It was inspired by G. Her- glotz in Göttingen, for whom and for whose mathematical style Fritz John had a great admiration. Later, in 1955, Fritz Obituaries John developed this topic in a beautiful book, Plane waves and spherical means, which made this circle of problems and their solution widely known. The book also contains Fritz John, 1910–1994 an elegant construction of the fundamental solution for par- Fritz John died in New Rochelle, NY, on February 10, 1994. tial differential equations. The later connection of the With his death the mathematical community lost an out- Radon transform to tomography is well known, although standing analyst whose remarkable and original work will this aspect was never pursued by F. John. His goal was to continue to influence and inspire mathematicians in the lay the foundations and make the first approaches. future. One of the most striking contributions of Fritz John is Fritz John was born June 14, 1910, in Berlin. He spent his seminal paper on rotation and strain in 1961, which led his school years in Danzig (nowadays Gdansk, Poland) and him to introduce the space of functions of bounded mean subsequently studied in Göttingen, where, after four years, oscillations as well as the concept of quasi-isometric map- he received his Ph.D. in 1933. This was the year the Hitler pings. Motivated by problems of elasticity theory, he raised regime began having its devastating effect on Germany, on some basic geometrical questions: What can be said about science, and, in particular, on the university in Göttingen. mappings of the Euclidean space (or domains in it) having F. John’s life was immediately deeply affected by this event, “small strain”, that is, mappings for which the Jacobian, and it was only through good luck and the help of colleagues multiplied from the left by its transpose, differs only lit- that John was able to receive his degree. His official advi- tle from the identity? From this local condition one can infer sor, as one would say in the U.S., was Courant, who was that in the maximum norm the mapping differs little from kicked out of his professorship that year; it was Courant’s a rigid motion—at least if the domain is not too slender. student, Franz Rellich, who took over the task of granting Next, John raised the question whether the first derivatives the degree to Fritz John. also deviate little from a constant matrix and showed that During the same year, and under tense political cir- this cannot be expected if one employs the maximum cumstances, Fritz John and Charlotte Woellmer were mar- norm. However, such a statement is true in the Lp-norm ried in Göttingen and left the country in 1934 for Cam- for any p. More precisely, one should use the so-called bridge, England. In 1935 he succeeded in obtaining an BMO-norm, and it is at this point that F. John was led to assistant professorship at the University of Kentucky, introduce the class of functions of “bounded mean oscil- where he stayed for eight years. He subsequently served lations” which became so important soon after he discov- for over two years at the Aberdeen Proving Ground as a ered them. It was C. Fefferman who subsequently identi- mathematician for the U.S. War Department. After the war fied this function space as the long-sought-after dual of the in 1946, John received a position at New York University, Hardy-space H1. This discovery made the space of BMO where he joined Courant, Friedrichs, and Stoker in build- functions a basic tool in harmonic analysis as well as in ing the institute which later became the Courant Institute other areas of analysis, and by now more than one hun- of Mathematical Sciences. Here his most important work dred publications have appeared on the subject. Through was created, and aside from a year (1950–1951) spent at the work of A. Garsia, Gundy, Burkholder, and others, this the National Bureau of Standards, he remained at this In- topic entered probability theory, and the relevant results stitute until he retired in 1981. In fact, he remained active were formulated in terms of martingale theory. at the Institute as Professor Emeritus.
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