Contemporary Mathematicians. Boston-Basel-Stuttgart: Birkhäuser. Vol. 1: 427 p.; Vol. 2: 608 p. Set: DM 475.00 (1986).

The first volume of these selecta begins with a brief but well-written and extremely interesting life of K. O. Friedrichs by Constance Reid. The publications of Friedrichs (spanning the period 1927-1982) are listed. They are categorized as Published Papers, Books, Lecture Notes, and Reports. For ease of reference, those items included in these selecta are clearly identified. With but one exception from the Reports section, all the items included in the present collection are from the Published Papers. The remainder of the first volume consists of thirteen papers in partial differential equations with commentaries on each of the papers by Peter Lax. Where appropriate, also included are the author’s subsequent corrections and on occasion additional corrections may be found in the relevant commentary. Both the German original [Math. Ann. 100, 32-74 (1928)] and the English translation [IBM J. Res. Dev. 11, 215-234 (1967;

Zbl 0145.404)] of the {\it R. Courant}, {\it K. Friedrichs} and {\it H. Lewy} paper ”On the partial difference equations of mathematical physics” are included [the table of contents contains an erroneous version of the title of the English version].
Volume two contains seven papers in Spectral Theory with commentaries by Tosio Kato, three papers in Elasticity with commentaries by Fritz John, two papers in Asymptotics with commentaries by Wolfgang Wasow, two papers in Magnetohydrodynamics preceded by Harold Weitzner’s article ”Contributions to magnetohydrodynamics”, two papers involving Variational problems with commentaries by Louis Nirenberg, and a miscellaneous section containing six papers (three of which have commentaries by Louis Nirenberg or Peter Lax). The final principal section of the second volume consists of David Isaacson’s article ”Contributions to quantum mechanics”, adapted from a talk at the memorial gathering for Professor Friedrichs in 1983.
The various commentaries are particularly interesting and valuable in that they generally provide important background material on the particular paper, its contents, Friedrichs’ originality and methodology, what inspired the paper, why it was written, and how it fits in. Among the selecta of the second volume are Friedrichs’ 1954 Gibbs Lecture, ”Asymptotic phenomena in mathematical physics” [Bull. Am. Math. Soc. 61, 485-504 (1955;

Zbl 0068.164)], and his 1979 von Neumann Lecture to the Society for Industrial and Applied Mathematics, ”Von Neumann’s Hilbert space theory and partial differential equations” [SIAM Rev. 22, 486-493 (1980;

Zbl 0457.35002)].