Biographical Memoirs Volume 67 (1995) / Chapter Skim
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Kurt Otto Friedrichs
Kurt Otto Friedrichs
Pages 130-145
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From page 131... ...
PART I: ElFE Kurt Otto Friedrichs was born in Kiel, Germany, on September 2S, 1901, but moved before his school days to Dusseldorf. He came from a comfortable background, his father being a well-known lawyer.
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Those first three papers demonstrate most of Friedrichs's lifetime in mathematics the first on the fundamental laws of the nature of matter, the second on applied mathematics viewed through analysis, and the third on basic theorems of wave propagation. The paper on hyperbolic partial differential equations led naturally to what turned out to be one of the bestknown and most used results of mathematics of the time ~ ~ 92S,2)
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From page 133... ...
There is scarcely a talk or a paper on modeling phenomena governed by so-callecl explicit difference schemes where this number does not come up. Friedrichs was interested, however, in proving existence theorems for partial differential equations by letting the mesh size and time step become vanishing small.
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to call his "other foot" namely, doing applied mathematics. On the whole, until the end of the Second World War his main contributions were in fluid dynamics with Courant and in elasticity with i.
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He published five monographs, which inspired a number of tociay's mathematical physicists, especially in the circle of Olga Ladyzhenskaya and Ludwig Fadeev in Russia. All the time as the spirit moved him he would do a basic piece for applied mathematics or a big chunk of writing for the famous Courant-Hilbert2 volume 2, completed in German in 1937 but essentially rewritten in English by many of the faculty of the burgeoning institute that was to become the Courant Institute in the early sixties.
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While afternoon teas as a fundamental ingredient of the intellectual life of a mathematician had been conceived at the ] :nstitute for Advanced Study in Princeton, Friedrichs carried the idea to the surroundings of NYU with his imposing principles.
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, and symmetric positive systems (1958~. All of these papers might be considered natural applications of the watershed result (1944)
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The result is the existence and uniqueness for all time of a solution to mixed initial boundary value problems for very wide classes of initial data and boundary conditions. The third major result is on "Symmetric Positive linear Differential Equations" ~1958)
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From page 139... ...
A remarkably wide variety of classical and nonclassical ones, such as various boundary value problems for a certain class of elliptic systems, the Cauchy problem for a certain class of hyperbolic equations, mixed initial boundary value problems for hyperbolic equations, and, last but not least, certain boundary value problems for equations of mixed type, such as Tricomi's equation, are symmetric positive. Friedrichs's main motivation was to treat systematically equations of mixed type and, as he often said, to establish a method of proof that was "deaf," as he put it, to changes of type anct would at the same time yield the number and kinds of boundary conditions necessary for well-posed problems.
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In his basic book on quantum mechanics van Neumann hac! identified the states of a quantum mechanical system with unit vectors in a Hilbert space and observables as self-adjoint operators.
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This paper is a contribution to one of the great controversies of twentieth-century physics, the debate between Niels Bohr and Albert Einstein over the completeness of quantum mechanics. Einstein felt that the laws of nature should be deterministic or causal, and for this reason he felt the quantum mechanical notion of the state of a particle was incomplete.
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From page 142... ...
Taken altogether, as one looks at Friedrichs's very extensive list of publications, one cannot help but be struck by the variety of ways and the number of times Frieclrichs broke new ground and then, with the passage of only a few years, how many of his ideas were absorbed into modern analysis and applied mathematics and became standard, so that it is almost forgotten today that they were Friedrichs's. As ~ write this, the spirit of Friedrichs hangs over me fussing over the details that are not quite right and reminc3ing me that T have left out this and ~ should have put in that, but ~ remind him that it was he who said, "Open your own newly published work on any random page and you will find a mistake." For those who wouIcl like to read his works in detail, ~ refer to the Selecta published by Birkhauser
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Storungstheorie der Spektralzerlegung. Mathematische Annalen 113 (1936)
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Lewy. Uber die Eindeutigkeit und das Abhangigkeitsgebiet der Losungen beim Anfangswertproblem linearer hyperbolischer Differentialgleichungen.
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61~6~:485-504. 1958 Symmetric positive linear differential equations.
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