Tauberian Theory

I The Hardy-Littlewood Theorems.- II Wiener's Theory.- III Complex Tauberian Theorems.- IV Karamata's Heritage: Regular Variation.- V Extensions of the Classical Theory.- VI Borel Summability and General Circle Methods.- VII Tauberian Remainder Theory.- References.

Education: Universities of Leiden and Utrecht, Mathematics and Physics, 1940--49 (with war-time interruptions)Ph.D. in Mathematics, Leiden, 1949Regular professorships (Mathematics)Technical University Delft (Netherlands), 1951-(Jan)1953University of Wisconsin (Madison), (Feb)1953--64(Chairman, Program in Applied Mathematics and Engineering Physics, 1956--61)University of California San Diego (La Jolla), 1964--74 (Chairman, Dept of Mathematics, 1971--73)University of Amsterdam, 1974--(Jan)93 (Director, Math. Institute, 1980--83) Temporary and visiting positionsMathematical Center, Amsterdam, 1947--49Purdue University, Acad. yrs 1949--51University of Michigan, Summer 1950Stanford University, Acad. yr 1961--62 and several summersClaremont Graduate School, Sep. 1969 -- Jan. 1970University of Oregon, Summer 1970Imperial College, London, Acad. yr 1970--71Technical University Eindhoven, Summer 1971California Institute of Technology, Spring 1988Bar-Ilan University (Israel), Spring 1992 Honors and special assignmentsReynolds' award for outstanding teaching of future engineers, University of Wisconsin, 1956Elected Fellow Amer. Assoc. Adv. Science, 1961Chairman, American Mathematical Society Summer Research Institute on "Entire functions and related parts of analysis", La Jolla, 1966Member, KNAW (Royal Netherlands Academy of Arts and Sciences) since 1975Honorary doctorate, University of Gothenburg (Sweden), 1978Chairman, Wiskundig Genootschap (Netherlands Mathematical Society), 1982--84Lester R. Ford Prize (1987) and Chauvenet Prize (1989) for mathematical exposition (Mathematical Association of America)Elected honorary member, Netherlands Math. Soc., 1998Honorary member, Amer. Math. Society Editor or co-editor of various mathematical journals and of conference proceedings at one time or another

From the reviews:



"The purpose of the monograph under review is to treat the principal Tauberian theorems in various categories by adopting the author's personal point of view which emphasizes the distributional aspects ... . the book carefully collects a rich amount of material on this topic. ... provides a detailed survey of almost all aspects of Tauberian theory. It will adopt a major position in the mathematical literature presently available on the various fields of summability methods." (Walter Schempp, Zentralblatt MATH, Vol. 1056, 2005)

"Typically a Tauberian Theorem states that the asymptotic behaviour of certain 'moving averages' is comparable for a large family of convolution kernels. ... One cannot do justice to a big volume like this by listing all the important results provided. It is certainly the reference work in the field for the years to come, hopefully inspiring continued research ... ." (H. G. Feichtinger, Internationale Mathematische Nachrichten, Issue 203, 2006)

"The aim of this monograph is 'to treat the principal Tauberian theorems in various categories and to provide attractive proofs.' ... Altogether, this volume treats an amazing variety of results. It will be an important reference for experts as well as anyone using Tauberian theorems, such as analytic number theorists." (Ch. Baxa, Monatshefte für Mathematik, Vol. 148 (2), 2006)

"Tauberian theory deals with the problem of finding conditions under which a summable series is actually convergent. ... A large bibliography and a substantial index round out the book. All in all, this is a well-written, well laid out, interesting monograph, essential to anyone involved in Tauberian theory and related topics. Highly recommended!" (B. Kirstein, Zeitschrift für Analysis und ihre Anwendungen, Vol. 24 (4), 2005)

"It is a monumental treatise, long years in the making, that covers the realm of Tauberian theory and its applications. ...the