Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF

Book Information

Author: Jacob Korevaar
Title: Tauberian theory, a century of developments
Additional book information Springer-Verlag, Berlin, Heidelberg, 2004, xv+483 pp., ISBN 3-540-21058-X, $109.00


References [Enhancements On Off] (What's this?)

  • 1. David Borwein, Tauberian theorems concerning Laplace transforms and Dirichlet series, Arch. Math. (Basel) 53 (1989), no. 4, 352–362. MR 1015999 (91e:40006), http://dx.doi.org/10.1007/BF01195215
  • 2. G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620 (11,25a)
  • 3. G.H. Hardy and J.E. Littlewood, Tauberian theorems concerning power series and Dirichlet's series whose coefficients are positive, Proc. London Math. Soc. (2) 13 (1914), 174-191.
  • 4. G.H. Hardy and J.E. Littlewood, Theorems concerning the summability of series by Borel's exponential method, Rend. Palermo 41 (1916), 36-53.
  • 5. S. Ikehara, An extension of Landau's theorem in the analytic theory of numbers, J. Math. and Phys. M.I.T. (2) 10 (1931), 1-12.
  • 6. J. Karamata, Über die Hardy-Littlewoodschen Umkehrungen des Abelschen Stetigkeitssatzes, Math. Z. 32 (1930), 319-320.
  • 7. J. Karamata, Neuer Beweis und Verallgemeinerung der Tauberschen Sätze, welche die Laplacesche Transformation betreffen, Math. Z. 164 (1931), 319-320.
  • 8. B. I. Korenblyum, On the asymptotic behavior of Laplace integrals near the boundary of a region of convergence, Dokl. Akad. Nauk SSSR (N.S.) 104 (1955), 173–176. MR 0074550 (17,605a)
  • 9. R. Schmidt, Über divergente Folgen und lineare Mittelbildungen, Math. Z. 22 (1925), 89-152.
  • 10. R. Schmidt, Umkersätze des Borelschen Summierungsverfahren, Schriften Köningsberg 1 (1925), 205-256.
  • 11. A. Tauber, Ein Satz aus der Theorie der uneindliche Reihen, Monatsh. Math. u. Phys. 8 (1897), 273-277.
  • 12. T. Vijayaraghavan, A Tauberian theorem, J. London Math. Soc. (1) 1 (1926), 113-120.
  • 13. T. Vijayaraghavan, A theorem concerning the summability of series by Borel's method, Proc. London Math. Soc. (2) 27 (1928), 316-326.
  • 14. David Vernon Widder, The Laplace Transform, Princeton Mathematical Series, v. 6, Princeton University Press, Princeton, N. J., 1941. MR 0005923 (3,232d)
  • 15. Helmut Wielandt, Zur Umkehrung des Abelschen Stetigketissatzes, Math. Z. 56 (1952), 206–207 (German). MR 0050038 (14,265i)
  • 16. Norbert Wiener, Tauberian theorems, Ann. of Math. (2) 33 (1932), no. 1, 1–100. MR 1503035, http://dx.doi.org/10.2307/1968102


Review Information

Reviewer: D. Borwein
Affiliation: University of Western Ontario
Email: dborwein@uwo.ca
Journal: Bull. Amer. Math. Soc. 42 (2005), 401-406
PII: S 0273-0979(05)01054-2
Published electronically: March 30, 2005
Review copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.