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An application of a general Tauberian remainder theorem

Arkiv för Matematik, 1975
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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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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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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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TAUBERIAN THEOREMS WITH A REMAINDER FOR LAPLACE TRANSFORMS IN THE PLANE

Mathematics of the USSR-Sbornik, 1983
General theorems are proved that for certain classes of (complex-valued) functions enable us to find an asymptotic expansion of as from an asymptotic expansion of its Laplace transform (as ) with respect to a domain having the origin of coordinates as an adherent point. A number of previous results are obtained as special cases.Bibliography: 3 titles.
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The remainder in a gap Tauberian theorem for Abel summability

Mathematical Proceedings of the Cambridge Philosophical Society, 1977
Using Pitt's Tauberian classes and a theorem of Pitt (3), Krishnan(2) has recently obtained a gap Tauberian theorem for (Aα) summability. We recall briefly the notation introduced in (2). Letand assume that the series a(t) and A(t) converge for all t > 0.
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Tauberian theorems with remainder for summation methods of the Gel'fand and Cesaro type

Ukrainian Mathematical Journal, 1989
Tauberian theorems on sequences from a linear locally convex space F are proved for Hölder and Cesàro methods. By special choice of F some earlier results of G. H. Hardy, R. Schmidt, N. A. Davydov and G. Kangro can be obtained from these theorems. Choosing the space of all continuous \(2\pi\)-periodic functions for F the author gives a result for ...
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