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A Tauberian Remainder Theorem with Applications to Lambert Summability.

MATHEMATICA SCANDINAVICA, 1974
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TWO TAUBERIAN REMAINDER THEOREMS FOR THE CESÀRO METHOD OF SUMMABILITY

Proceedings of the Estonian Academy of Sciences. Physics. Mathematics, 2000
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An application of a general Tauberian remainder theorem

Arkiv för Matematik, 1975
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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.
Wolfram Luther
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A Tauberian theorem with remainder for the Laplace transform and its application to the riemann zeta-function

Ukrainian Mathematical Journal, 1991
A new variant of a Tauberian theorem with remainder is proved for the Laplace transform in the plane, using the L1 metric. A connection between the divisor problem and the growth of the zeta-function in the critical strip is established.
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Tauberian Theorems with Remainder

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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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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Estimation of Coefficients of Univalent Functions by a Tauberian Remainder Theorem

Journal of the London Mathematical Society, 1974
Peer Reviewed ; http://deepblue.lib.umich.edu/bitstream/2027.42/135160/1/jlms0279 ...
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Tauberian theorems with remainder for (H, p, α, β)-and (C, p, α, β)-methods of summation of functions of two variables

Ukrainian Mathematical Journal, 1999
We consider a general method of obtaining Tauberian theorems with remainder for Holder- and Cesarotype methods of summation.
V. M. Aldanov, G. O. Mikhalin
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