Results 31 to 40 of about 733 (210)

A tauberian theorem for the conformal bootstrap

Journal of High Energy Physics, 2017
For expansions in one-dimensional conformal blocks, we provide a rigorous link between the asymptotics of the spectral density of exchanged primaries and the leading singularity in the crossed channel. Our result has a direct application to systems of SL(
Jiaxin Qiao, Slava Rychkov
doaj   +1 more source

On a Tauberian theorem of Landau [PDF]

Proceedings of the American Mathematical Society, 1958
T(x) = A(-) = xlog x+ bx+ o(x) nfix n with b a constant, theni (1) c1x < A(x) < c2x, where c1 and c2 are positive constants. This gives Tschebyschef's theorem if Mwe take A(x) = A(x) and use the fact that log [x]! = x log x x + O(log x). Landau states that if only the condition T(x) = x log x + O(x) is assumed, then (1) does not follow, a remark whose ...
openaire   +1 more source

Distributional versions of Littlewood's Tauberian theorem

, 2010
summary:We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We employ two types of Tauberian hypotheses; the first kind involves distributional boundedness,
Vindas Diaz, Jasson, Totur T., Estrada, Ricardo, Erdem Y., Vindas, Jasson, Çanak T.   +5 more
core   +1 more source

A Tauberian Theorem and Analogues of the Prime Number Theorem

, 1968
In 1945 Ingham (3) proved the following Tauberian theorem: if ƒ is a non-decreasing, non-negative function on [1, ∞) and1then ƒ(x) ∼ cx. His proof is based on the non-vanishing of the Riemann zeta-function, ζ (s), on the line , and uses Pitt's form of ...
T. M. K. Davison
core   +1 more source

A tauberian theorem for distributional point values

, 2008
We give a tauberian theorem for boundary values of analytic functions. We prove that if f is an element of D' (a, b) is the distributional limit of the analytic function F defined in a region of the form (a, b) x (0, R), if F (x(0) + iy) -> gamma as y ->
Vindas Diaz, Jasson, Estrada, Ricardo, Vindas, Jasson   +2 more
core   +1 more source

Esterlè's proof of the tauberian theorem for Beurling algebras [PDF]

, 1981
Recently in this Journal J. Esterlé gave a new proof of the Wiener Tauberian theorem for $L^1({\bf R})$ using the Ahlfors-Heins theorem for bounded analytic functions on a half-plane.
Dales, H.G., Dales, H. G., H. G. Dales, W. K. Hayman, Hayman, W. K.   +4 more
core   +1 more source

A Tauberian Theorem for Double Cesàro Summability Method

International Journal of Mathematics and Mathematical Sciences, 2016
We have generalized Littlewood Tauberian theorems for (C,k,r) summability of double sequences by using oscillating behavior and de la Vallée-Poussin mean.
Bidu Bhusan Jena, Susanta Kumar Paikray, Umakanta Misra   +2 more
doaj   +1 more source

Tauberian-Cardy formula with spin

Journal of High Energy Physics, 2020
We prove a 2 dimensional Tauberian theorem in context of 2 dimensional conformal field theory. The asymptotic density of states with conformal weight (h, h ¯ $$ \overline{h} $$ ) → (∞, ∞) for any arbitrary spin is derived using the theorem.
Sridip Pal, Zhengdi Sun
doaj   +1 more source

Littlewood, Paley and almost‐orthogonality: a theory well ahead of its time

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract The classic paper by Littlewood and Paley [J. Lond. Math. Soc. (1), 6 (1931), 230–233] marked the birth of Littlewood–Paley theory. We discuss this paper and its impact from a historical perspective, include an outline of the results in the paper and their subsequent significance in relation to developments over the last century, and set them ...
Anthony Carbery
wiley   +1 more source