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An extension of the integral test
Author(s):
Ana
Lía
Durán;
Ricardo
Estrada
Journal:
Proc. Amer. Math. Soc.
127
(1999),
1745-1751.
MSC (1991):
Primary 26A06, 40A10, 46F10
Posted:
February 11, 1999
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Abstract:
We identify a class of functions for which an extension of the well known integral test holds, namely, the series  is Cesàro summable if and only if the integral  is. We also give the corresponding multidimensional results.
References:
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- J. Boersma, A nonharmonic trigonometric series, solution of Problem 94-12, SIAM Review 37 (1995), 443-445.
- 2.
- A. L. Durán and R. Estrada, The analytic continuation of moment functions and of zeta functions, preprint, San José, 1997.
- 3.
- A. L. Durán, R. Estrada and R. P. Kanwal, Extensions of the Poisson summation formula, J. Math. Anal. Appl. 218 (1998), 581-606. CMP 98:08
- 4.
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- 5.
- R. Estrada, J. M. Gracia-Bondía and J. C. Várilly, On summability of distributions and spectral geometry, Commun. Math. Phys. 191 (1998), 219-248. CMP 98:07
- 6.
- R. Estrada and R. P. Kanwal, Asymptotic Analysis: a Distributional Approach, Birkhäuser, Boston, 1994. MR 95g:46071
- 7.
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- 8.
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- 10.
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- 11.
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Additional Information:
Ana
Lía
Durán
Affiliation:
Escuela de Matemática, Universidad de Costa Rica, 2060 San José, Costa Rica
Email:
analiad@emate.ucr.ac.cr
Ricardo
Estrada
Affiliation:
Escuela de Matemática, Universidad de Costa Rica, 2060 San José, Costa Rica
Email:
restrada@cariari.ucr.ac.cr
DOI:
10.1090/S0002-9939-99-04911-4
PII:
S 0002-9939(99)04911-4
Keywords:
Integral,
series,
summability
Received by editor(s):
September 12, 1997
Posted:
February 11, 1999
Communicated by:
Frederick W. Gehring
Copyright of article:
Copyright
1999,
American Mathematical Society
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