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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,
$109.00$
David Borwein, Tauberian theorems concerning Laplace transforms and Dirichlet series, Arch. Math. (Basel) 53 (1989), no. 4, 352–362. MR 1015999, DOI 10.1007/BF01195215
G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620
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.
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
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.
David Vernon Widder, The Laplace Transform, Princeton Mathematical Series, vol. 6, Princeton University Press, Princeton, N. J., 1941. MR 0005923
Helmut Wielandt, Zur Umkehrung des Abelschen Stetigketissatzes, Math. Z. 56 (1952), 206–207 (German). MR 50038, DOI 10.1007/BF01175034
Norbert Wiener, Tauberian theorems, Ann. of Math. (2) 33 (1932), no. 1, 1–100. MR 1503035, DOI 10.2307/1968102
- 1.
- D. Borwein, Tauberian theorems concerning Laplace transforms and Dirichlet series, Arch. Math. (Basel) 53 (1989), 352-362. MR 1015999
- 2.
- G.H. Hardy, Divergent Series, Oxford, 1949. MR 0030620
- 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
- 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
- 15.
- H. Wielandt, Zur Umkehrung des Abelschen Stetigkeitssatzes, J. Reine Angew Math. 56 (1952), 27-39. MR 0050038
- 16.
- N. Wiener, Tauberian theorems, Annals of Math. (2) 33 (1932), 1-100. MR 1503035
Review Information:
Reviewer:
D. Borwein
Affiliation:
University of Western Ontario
Email:
dborwein@uwo.ca
Journal:
Bull. Amer. Math. Soc.
42 (2005), 401-406
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.
