Results 21 to 30 of about 10,861 (121)

The formal Laplace-Borel transform of Fliess operators and the composition product

International Journal of Mathematics and Mathematical Sciences, 2006
The formal Laplace-Borel transform of an analytic integral operator, known as a Fliess operator, is defined and developed. Then, in conjunction with the composition product over formal power series, the formal Laplace-Borel transform is shown to provide ...
Yaqin Li, W. Steven Gray
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Topological computation of some Stokes phenomena on the affine line [PDF]

, 2019
Let $\mathcal M$ be a holonomic algebraic $\mathcal D$-module on the affine line, regular everywhere including at infinity. Malgrange gave a complete description of the Fourier-Laplace transform $\widehat{\mathcal M}$, including its Stokes multipliers at
D'Agnolo, Andrea, Hien, Marco, Morando, Giovanni, Sabbah, Claude   +3 more
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On a q—Analog of a Singularly Perturbed Problem of Irregular Type with Two Complex Time Variables

Mathematics, 2019
The analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain are constructed and studied from an asymptotic point of view with respect to the perturbation parameter.
Alberto Lastra, Stéphane Malek
doaj   +1 more source

Analytic continuation and perturbative expansions in QCD [PDF]

, 2001
Starting from the divergence pattern of perturbative quantum chromodynamics, we propose a novel, non-power series replacing the standard expansion in powers of the renormalized coupling constant $a$.
Caprini, Irinel, Fischer, Jan
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Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field [PDF]

, 2001
We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power series in the ...
A. LoSurdo, A. Maquet, A. van Wijngaarden, B.G. Adams, C. Itzykson, C.A. Nicolaides, C.M. Bender, D. Broadhurst, D. Farrelly, E. Caliceti, E. Caliceti, E. Caliceti, E. Caliceti, E. Luc-Koenig, E. Luc-Koenig, E.J. Weniger, F.M. Fernández, G. Alvarez, G. Alvarez, G. Alvarez, G.A. Baker, G.V. Dunne, H. Rottke, H. Silverstone, H. Silverstone, H.J. Silverstone, H.S. Silverstone, I. Caprini, I. Caprini, I.W. Herbst, I.W. Herbst, J. C. LeGuillou, J. Fischer, J. Fischer, J. Schwinger, J. Stark, J. Zamastil, J. Zinn-Justin, J.C. LeGuillou, J.C. LeGuillou, J.E. Avron, J.R. Oppenheimer, L. Benassi, L. Benassi, L. Benassi, M. Beneke, M. Hehenberger, M. Reed, M.H. Alexander, M.I. Eides, N.A. Gushina, P. Froelich, P.A. Ra̧czka, P.J. Mohr, P.J. Mohr, P.M. Koch, R. Guida, R. Guida, R. Seznec, R.J. Damburg, R.J. Damburg, R.J. Damburg, S. Graffi, S. Graffi, S. Wolfram, T. Bergeman, T. Yamabe, U.D. Jentschura, U.D. Jentschura, U.D. Jentschura, U.D. Jentschura, U.D. Jentschura, U.D. Jentschura, Ulrich D. Jentschura, V. Franceschini, V.B. Berestetskii, V.V. Kolosov, V.V. Kolosov, W. Greiner, W. Heisenberg, W.L. Glab, W.L. Glab, W.R. Johnson   +82 more
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Resurgence of the Euler-MacLaurin summation formula [PDF]

, 2007
The Euler-MacLaurin summation formula relates a sum of a function to a corresponding integral, with a remainder term. The remainder term has an asymptotic expansion, and for a typical analytic function, it is a divergent (Gevrey-1) series.
Costin, Ovidiu, Garoufalidis, Stavros
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Analytic structure in the coupling constant plane in perturbative QCD

, 2003
We investigate the analytic structure of the Borel-summed perturbative QCD amplitudes in the complex plane of the coupling constant. Using the method of inverse Mellin transform, we show that the prescription dependent Borel-Laplace integral can be cast,
A. Sokal, A.H. Mueller, D. Broadhurst, G. Cvetič, G. Parisi, I. Caprini, I. Caprini, I. Caprini, I. Caprini, Irinel Caprini, J. Fischer, Jan Fischer, M. Beneke, M. Beneke, M. Beneke, M. Beneke, M. Neubert, N.N. Khuri, P. Ball, T. Lee   +19 more
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Improved Conformal Mapping of the Borel Plane [PDF]

, 2000
The conformal mapping of the Borel plane can be utilized for the analytic continuation of the Borel transform to the entire positive real semi-axis and is thus helpful in the resummation of divergent perturbation series in quantum field theory.
Altarelli G, Baker G A, Bender C M, Broadhurst D, Caprini I, Gerhard Soff, J Fischer, Jentschura U D, Jentschura U D, Jentschura U D, LeGuillou J C, LeGuillou J C, Pindor M, Raczka P A, Seznec R, Ulrich D Jentschura, Zinn-Justin J   +16 more
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Resummation in QFT with Meijer G-functions [PDF]

, 2018
We employ a recent resummation method to deal with divergent series, based on the Meijer G-function, which gives access to the non-perturbative regime of any QFT from the first few known coefficients in the perturbative expansion.
Antipin, Oleg, Maiezza, Alessio, Vasquez, Juan Carlos   +2 more
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Introduction to 1-summability and resurgence [PDF]

, 2014
This text is about the mathematical use of certain divergent power series. The first part is an introduction to 1-summability. The definitions rely on the formal Borel transform and the Laplace transform along an arbitrary direction of the complex plane.
Sauzin, David
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