An extension of the integral test-Reference-Cited by-同舟云学术

An extension of the integral test

Published:1999-02-11 Issue:6 Volume:127 Page:1745-1751
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Durán Ana,Estrada Ricardo

Abstract

We identify a class of functions for which an extension of the well known integral test holds, namely, the series ∑ k = 1 ∞ ϕ ( k ) \sum _{k=1}^{\infty }\phi (k) is Cesàro summable if and only if the integral ∫ 1 ∞ ϕ ( x ) d x \int _{1}^{\infty }\phi (x)\,dx is. We also give the corresponding multidimensional results.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1999-127-06/S0002-9939-99-04911-4/S0002-9939-99-04911-4.pdf

Reference11 articles.

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4. R. Estrada, The Cesàro behavior of distributions, Proc. Roy. Soc. London A (to appear).

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.

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