Results 121 to 130 of about 183 (170)
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Mathematical Notes, 1974
A lemma is formulated on the asymptotic behavior of functions of class “R”; this lemma is then used for strengthening a well-known Tauberian theorem of Keldysh type for a two-sided Stieltjes transform.
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A lemma is formulated on the asymptotic behavior of functions of class “R”; this lemma is then used for strengthening a well-known Tauberian theorem of Keldysh type for a two-sided Stieltjes transform.
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The Annals of Mathematics, 1932
Nachdem N. Wiener in einer früheren Abhandlung [J. Math. Phys., Mass. Inst. Technol. 8, 161--184 (1928; JFM 54.0241.01)] die Theorie der Fourierschen Transformierten in den Problemkreis der Mittelungsumkehrsätze (Tauberian theorems) eingeführt hatte, wird hier der gleiche Gegenstand ausführlicher und auf einer breiteren Basis erneut behandelt.
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Nachdem N. Wiener in einer früheren Abhandlung [J. Math. Phys., Mass. Inst. Technol. 8, 161--184 (1928; JFM 54.0241.01)] die Theorie der Fourierschen Transformierten in den Problemkreis der Mittelungsumkehrsätze (Tauberian theorems) eingeführt hatte, wird hier der gleiche Gegenstand ausführlicher und auf einer breiteren Basis erneut behandelt.
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A Generalized Tauberian Theorem
Canadian Journal of Mathematics, 1958Let {s(n)} be a real sequence and let x be any number in the interval 0 < x ⩽ 1. Representing x by a non-terminating binary decimal expansion we shall denote by {s(n,x)} the subsequence of {s(n)} obtained by omitting s(k) if and only if there is a 0 in the decimal place in the expansion of x. With this correspondence it is then possible to speak of “
Keogh, F. R., Petersen, G. M.
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A Tauberian Theorem for Partitions
The Annals of Mathematics, 1941The author's principal aim is to deduce the asymptotic formulas \[ p(n)\sim e^{\pi\sqrt{2n/3}}/4\sqrt 3 n,\quad q(n) \sim e^{\pi\sqrt{n/3}}/4\cdot 3^{\frac14}n^{\frac34},\quad n\to\infty, \] from reasonably simple properties of the generating functions for \(p(n)\) and \(q(n)\), the number of unrestricted partitions of \(n\) and the number of ...
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1994
Abstract This chapter concentrates on the more delicate Tauberian theorems for Borel-type methods.
Bruce Shawyer, Bruce Watson
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Abstract This chapter concentrates on the more delicate Tauberian theorems for Borel-type methods.
Bruce Shawyer, Bruce Watson
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Tauberian Theorems for Integrals
Canadian Journal of Mathematics, 1963When, for the generalized summation of series, we use A and B methods, giving A and B sums, respectively, we say that the A method is included in the B method, A ⊂ B, if the B sum exists and is equal to the A sum whenever the latter exists. A theorem proving such a result is called an Abelian theorem.
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Tauberian Theorems with Remainder
Journal of the London Mathematical Society, 1985Suppose 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 Theorems and the Central Limit Theorem
Annals of Probability, 1981 We prove Tauberian theorems for random walks with positive drift obeying the central limit theorem. The results include (i) conclusions involving certain averages, relevant to number-theoretic densities and extending results of Diaconis and Stein; (ii) pointwise conclusions, including the classical Borel-Tauber theorem and extending results of Schmaal,
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The Simplest Tauberian Theorem
Mathematical Notes, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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