Tauberian remainder theorem - Open Access .click

Journal of the London Mathematical Society, 1985
Suppose f and g are nondecreasing functions with finite Laplace transforms $\hat f$ and $\hat g$. In the paper we discuss conditions under which as $x\to \infty$, $\hat f(\frac{1}{x})-\hat g(\frac{1}{x})=0(a(x))$ implies $f(x)-g(x)=O(b(x))$ for certain classes of functions g(x),a(x) and b(x), thereby extending a result of \textit{A. E. Ingham}
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A Tauberian Remainder Theorem for the Hankel Transform

SIAM Journal on Mathematical Analysis, 1978
Using a general Parseval relation and the Wiener–Ganelius method, we give sharp Tauberian remainder results for the Hankel transform $F_\nu (x) = \int_0^\infty {\sqrt {xu} } J_\nu (xu)f(u)du$, $\nu \geqq {{ - 1} / 2}$. The remainder of $f(u)$ covers the whole range between $o(1)$ and $O(u^{ - 1} )$ which is a minorant for this transform.
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Tauberian Remainder-theorems.

1972
PhD ; Mathematics ; University of Michigan, Horace H. Rackham School of Graduate Studies ; http://deepblue.lib.umich.edu/bitstream/2027.42/187601/2/7306929 ...
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Tauberian theorems with remainder for Riesz and cesaro means

Ukrainian Mathematical Journal, 1984
Le premier et le deuxième théorème de cet article sont les théorèmes généraux de Tauber avec le reste pour la méthode de la sommabilité de Riesz et le troisième et le quatrième théorème sont les théorèmes généraux de Tauber avec le reste pour la méthode de la sommabilité de Cesàro.
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tauberian theorems
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weighted mean method
weighted general control modulo
tauberian remainder theorems

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