Mathematics from Leningrad to Austin. George G. Lorentz' selected works in real, functional and numerical analysis. Vol. 1. Ed. by Rudolph A. Lorentz
This is the first of two volumes [vol. 2 see below (Zbl 0874.01012)] containing approximately two thirds of the papers, published 1932 to 1997, by G. G. Lorentz (born 1910). They are edited by his son and, for several papers, co-author. An autobiography is augmented by remarks of the editor. Further contents: Complete bibliography; list of doctoral students; a report on mathematics at Leningrad, and the university life there (1928-1942); and three unpublished papers addressing a general audience. -- The work of G.G. Lorentz was written in the Soviet Union, in West Germany (after 1944), and in North America (since 1949), a considerable part of it with co-authors, among them K. Knopp, K. L. Zeller, P. Erdös, A. Robinson, H. Berens, S. Riemenschneider, M. v. Golitschek. With remarkable perseverance, and always keeping in touch with contemporary research of others, Lorentz has pursued several threads of 20th century real analysis. Lucidly written, the papers and the comments prepared for the present edition may serve as a guideline for developments during more than six decades. The theory of summability is reviewed by S. Baron and D. Leviatan. Main topics are matrix transformations, Tauberian conditions, summability functions, rearrangements, and orthogonal series. The papers on interpolation are commented by S. Riemenschneider who concentrates on papers concerning Birkhoff interpolation (also for splines). This review may also serve as an introduction to the subject and its rapid development since 1966.
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