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Hans Lewy (20 October 1904 – 23 August 1988) was an American mathematician, known for his work on partial differential equations and on the theory of functions of several complex variables.

Life

Lewy was born to a Jewish family in Breslau, Silesia, on October 20, 1904. He began his studies at the University of Göttingen in 1922, after being advised to avoid the more local University of Breslau because it was too old-fashioned, supporting himself during the Weimar hyperinflation by a side job doing railroad track maintenance.

He retired from Berkeley in 1972, and in 1973 became one of two Ordway Professors of Mathematics at the University of Minnesota. He died on August 23, 1988, in Berkeley.

Lewy is known for his contributions to partial differential equations. In 1957, his famous example of a first-order linear partial differential operator, <math>L= (\partial_{x_1}+i\partial_{x_2})-2i(x_1+ix_2)\partial_{y_1}</math>, with complex coefficients for which the equation <math>Lu=f</math> has no local solutions unless <math>f</math> is real analytic was so stunning and unexpected that it redirected the field of partial differential equations, as well as shaping modern analysis in a significant way. Based on this example, Louis Nirenberg, Lars Hörmander, Francois Treves, Nils Dencker, etc. developed a theory of local solvability for pseudo-differential equations.

He also worked on several complex variables in relation to nonlinear hyperbolic equations and elliptic equations, well-posedness for initial value problems of wave fronts (now commonly called Sobolev spaces) in the early 1930s, solutions of the classical problems of Hermann Weyl and Hermann Minkowski for analytical data (the original problem was solved by Louis Nirenberg in 1949 as part of his PhD thesis), the extendibility of minimal surfaces on and analytical nature of its boundaries which is fully free or in part, free boundary problems of water wave fronts in hydrodynamics, and the proof of quadratic reciprocity theorem in number theory from 'hydrodynamical' perspective.

Awards and honors

Lewy was elected to the National Academy of Sciences in 1964, and was also a member of the American Academy of Arts and Sciences.

A selection of his work, edited by David Kinderlehrer and including his most important works, was published as the two volume work and

  • . With biographical essays by Helen Lewy and Constance Reid, and commentaries on Lewy's work by Erhard Heinz, Peter D. Lax, Jean Leray, Richard MacCamy, Louis Nirenberg and François Treves.
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The following works are included in his "Selecta" in their original language or translated form.

  • . There are also two English translations of the 1928 German original paper: the first one is a translation from the German by Phyllis Fox, circulated as a research report: . The second one is a typographical improvement of the first, published by IBM as: . A freely downloadable version of this one can be found here
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See also

  • Lewy's example
  • Courant–Friedrichs–Lewy condition

References

  • .
  • . An audio interview, available at eCommons@Cornell from the [Eugene B. Dynkin Collection of Mathematics Interviews Eugene B. Dynkin Collection of Mathematics Interviews ].
  • . The biographical entry about Hans Lewy at the Enciclopedia Treccani.