Tauberian Theory

TRAMA

Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. The author shows the development of the theory from the beginning and his expert commentary evokes the excitement surrounding the early results. He shows the fascination of the difficult Hardy-Littlewood theorems and of an unexpected simple proof, and extolls Wiener's breakthrough based on Fourier theory. There are the spectacular "high-indices" theorems and Karamata's "regular variation", which permeates probability theory. The author presents Gelfand's elegant algebraic treatment of Wiener theory and his own distributional approach. There is also a new unified theory for Borel and "circle" methods. The text describes many Tauberian ways to the prime number theorem. A large bibliography and a substantial index round out the book.

SOMMARIO

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.

AUTORE

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

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9783642059193
• Collana: Grundlehren der mathematischen Wissenschaften
• Dimensioni: 235 x 155 mm
• Formato: Brossura
• Illustration Notes: XV, 483 p.
• Pagine Arabe: 483
• Pagine Romane: xv