Buch, Englisch, 483 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1940 g
A Century of Developments
Buch, Englisch, 483 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1940 g
Reihe: Grundlehren der mathematischen Wissenschaften
ISBN: 978-3-540-21058-0
Verlag: Springer Berlin Heidelberg
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Algebra Zahlentheorie
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
Weitere Infos & Material
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.
