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Book Review
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Book Information
Author(s):
Jacob Korevaar
Title:
Tauberian theory, a century of developments
Additional book information:
Springer-Verlag,
Berlin, Heidelberg,
2004,
xv+483,
$109.00,
ISBN 3-540-21058-X
References:
-
- 1.
- D. Borwein, Tauberian theorems concerning Laplace transforms and Dirichlet series, Arch. Math. (Basel) 53 (1989), 352-362. MR 1015999 (91e:40006)
- 2.
- G.H. Hardy, Divergent Series, Oxford, 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. Korenblum, On the asymptotic behaviour of Laplace integrals near the boundary of a region of convergence (Russian), Dokl. Akad. SSSR (NS) 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.
- D.V. Widder, The Laplace Transform, Princeton, 1946. MR 0005923 (3,232d)
- 15.
- H. Wielandt, Zur Umkehrung des Abelschen Stetigkeitssatzes, J. Reine Angew Math. 56 (1952), 27-39. MR 0050038 (14,265i)
- 16.
- N. Wiener, Tauberian theorems, Annals of Math. (2) 33 (1932), 1-100. MR 1503035
Additional Information:
Reviewer(s):
D.
Borwein
Affiliation:
University of Western Ontario
Email:
dborwein@uwo.ca
Review Information:
Journal:
Bull. Amer. Math. Soc.
42
(2005),
401-406.
MSC
(2000):
Primary 40E05
PII:
S 0273-0979(05)01054-2
Posted:
March 30, 2005
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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