Author | Korevaar, Jacob. author |
---|---|

Title | Tauberian Theory [electronic resource] : A Century of Developments / by Jacob Korevaar |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004 |

Connect to | http://dx.doi.org/10.1007/978-3-662-10225-1 |

Descript | XV, 483 p. online resource |

SUMMARY

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

CONTENT

I The Hardyโ{128}{148}Littlewood Theorems -- II Wienerโ{128}{153}s Theory -- III Complex Tauberian Theorems -- IV Karamataโ{128}{153}s Heritage: Regular Variation -- V Extensions of the Classical Theory -- VI Borel Summability and General Circle Methods -- VII Tauberian Remainder Theory -- References

Mathematics
Mathematical analysis
Analysis (Mathematics)
Approximation theory
Fourier analysis
Integral transforms
Operational calculus
Sequences (Mathematics)
Number theory
Mathematics
Analysis
Sequences Series Summability
Approximations and Expansions
Fourier Analysis
Integral Transforms Operational Calculus
Number Theory