By Vincent Rivasseau (Chief Editor)

Articles during this volume:

1-47

Inverse Scattering at fastened strength in de Sitter–Reissner–Nordström Black Holes

Thierry Daudé and François Nicoleau

49-65

Linear Perturbations for the Vacuum Axisymmetric Einstein Equations

Sergio Dain and Martín Reiris

67-76

A Volumetric Penrose Inequality for Conformally Flat Manifolds

Fernando Schwartz

77-118

Asymptotes in SU(2) Recoupling idea: Wigner Matrices, 3j Symbols, and personality Localization

Joseph Ben Geloun and Razvan Gurau

119-152

Spectral research of an efficient Hamiltonian in Nonrelativistic Quantum Electrodynamics

Asao Arai

153-172

Uniform Convergence of Schrödinger Cocycles over basic Toeplitz Subshift

Qing-Hui Liu and Yan-Hui Qu

173-204

Loi de Weyl presque sûre pour un Système Différentiel en size 1

William Bordeaux Montrieux

205-277

On Breakdown standards for Nonvacuum Einstein Equations

Arick Shao

279-301

Further regulations at the Topology of desk bound Black Holes in 5 Dimensions

Stefan Hollands, Jan Holland and Akihiro Ishibashi

303-328

Fermi Coordinates, Simultaneity, and increasing house in Robertson–Walker Cosmologies

David Klein and Evan Randles

329-349

Existence of Dyons within the Coupled Georgi–Glashow–Skyrme Model

Fanghua Lin and Yisong Yang

351-395

Gauge Orbit kinds for Theories with Gauge staff O(n), SO(n) or Sp(n)

Alexander Hertsch, Gerd Rudolph and Matthias Schmidt

397-418

Exactly Solvable Schrödinger Operators

Jan Dereziński and Michał Wrochna

419-482

The Cauchy challenge on a attribute Cone for the Einstein Equations in Arbitrary Dimensions

Yvonne Choquet-Bruhat, Piotr T. Chruściel and José M. Martín-García

483-545

Topological Graph Polynomial and Quantum box conception half II: Mehler Kernel Theories

Thomas Krajewski, Vincent Rivasseau and Fabien Vignes-Tourneret

547-590

Homogeneous Schrödinger Operators on Half-Line

Laurent Bruneau, Jan Dereziński and Vladimir Georgescu

591-620

Dimension conception for Multimodal Maps

Godofredo Iommi and Mike Todd

621-677

Ground States within the Spin Boson Model

David Hasler and Ira Herbst

679-721

Aharonov–Bohm influence in Resonances of Magnetic Schrödinger Operators with Potentials with helps at huge Separation

Ivana Alexandrova and Hideo Tamura

723-741

Coulomb structures on Riemannian Manifolds and balance of Matter

Alberto Enciso

743-775

Random stroll on Surfaces with Hyperbolic Cusps

Hans Christianson, Colin Guillarmou and Laurent Michel

777-804

Divergences in Quantum box concept at the Noncommutative Two-Dimensional Minkowski area with Grosse–Wulkenhaar Potential

Jochen Zahn

805-827

Ground nation Representations of Loop Algebras

Yoh Tanimoto

829-847

The 1/N enlargement of coloured Tensor Models

Razvan Gurau

849-917

Future balance of the Einstein-Maxwell-Scalar box System

Christopher Svedberg

919-964

A type of Dust-Like Self-Similar options of the Massless Einstein–Vlasov System

Alan D. Rendall and Juan J. L. Velázquez

965-985

Areas and Volumes for Null Cones

James D. E. Grant

987-1017

Critical issues of Wang–Yau Quasi-Local Energy

Pengzi Miao, Luen-Fai Tam and Naqing Xie

1019-1025

Yamabe Numbers and the Brill–Cantor Criterion

Helmut Friedrich

1027-1053

On the Geometry of the Nodal traces of Eigenfunctions of the Two-Dimensional Torus

Jean Bourgain and Zeév Rudnick

1055-1079

Thermal results in Gravitational Hartree Systems

Gonca L. Aki, Jean Dolbeault and Christof Sparber

1081-1108

Lyapunov Exponents, Periodic Orbits and Horseshoes for Mappings of Hilbert Spaces

Zeng Lian and Lai-Sang Young

1109-1144

On Quantum Markov Chains on Cayley Tree II: section Transitions for the linked Chain with XY-Model at the Cayley Tree of Order Three

Luigi Accardi, Farrukh Mukhamedov and Mansoor Saburov

1145-1168

Associativity of box Algebras

Namhoon Kim

1169-1197

Quantization of aspect Currents alongside Magnetic limitations and Magnetic Guides

Nicolas Dombrowski, François Germinet and Georgi Raikov

1199-1226

From optimistic box idea to Fractional Stochastic Calculus. (I) An advent: tough direction thought and Perturbative Heuristics

Jacques Magnen and Jérémie Unterberger

1227-1319

Quantum Diffusion and Delocalization for Band Matrices with normal Distribution

László Erdős and Antti Knowles

1321-1347

The flooring nation strength of the Massless Spin-Boson Model

Abdelmalek Abdesselam

1349-1385

Resolvent Estimates for more often than not Hyperbolic Trapped Sets

Jared Wunsch and Maciej Zworski

1387-1415

Spacelike Localization of Long-Range Fields in a version of Asymptotic Electrodynamics

Andrzej Herdegen and Katarzyna Rejzner

1417-1429

Kochen–Specker units and Generalized Orthoarguesian Equations

Norman D. Megill and Mladen Pavičić

1431-1447

Recursion among Mumford Volumes of Moduli Spaces

Bertrand Eynard

1449-1489

Approximate KMS States for Scalar and Spinor Fields in Friedmann–Robertson–Walker Spacetimes

Claudio Dappiaggi, Thomas-Paul Hack and Nicola Pinamonti

1491-1538

Stability and Instability of utmost Reissner–Nordström Black gap Spacetimes for Linear Scalar Perturbations II

Stefanos Aretakis

1539-1570

Spectral conception for a Mathematical version of the vulnerable interplay: The Decay of the Intermediate Vector Bosons W±, II

Walter H. Aschbacher, Jean-Marie Barbaroux, Jérémy Faupin and Jean-Claude Guillot

1571-1599

Anderson Localization for a category of types with a Sign-Indefinite Single-Site strength through Fractional second Method

Alexander Elgart, Martin Tautenhahn and Ivan Veselić

1601-1612

Stochastic Description of a Bose–Einstein Condensate

Laura M. Morato and Stefania Ugolini

1613-1634

Semiclassical Propagation of Coherent States for the Hartree Equation

Agissilaos Athanassoulis, Thierry Paul, Federica Pezzotti and Mario Pulvirenti

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**Additional resources for Annales Henri Poincaré - Volume 12**

**Example text**

Of course it will not be the case for the scattering data. We also stress the fact that we have only assumed that X < X1 < A by convenience: the asymptotics of the derivative of the Jost functions fj (X, λ, z) are simpler under this condition. In order to obtain the asymptotics of the scattering data, we need to calculate the asymptotics of the Jost functions gj (X, λ, z). Since the procedure is the same as the one for the fj (X, λ, z), we give without proof the main steps to obtain the asymptotics of gj (X, λ, z), j = 1, 2, when z → +∞.

The Fourier Transform in z In Eqs. (23)–(24) the z dependence is clearly simpler than the ρ dependence. The equations are regular in z and the coefﬁcients of the differential operators do not depend on z. Hence, in order to factor out the z dependence we can 2 What is remarkable about this particular choice of coefficients is that, after a Fourier transform in z (Sect. 2) and a Hankel transform in ρ (Sect. 3), the resulting system can be reduced into a ordinary harmonic oscillator equation (in time) as is displayed in Eq.

1. f1+ (X, λ, z) = For X ∈]0, A[ and z ∈ C, − κ+ a+ iλ κ+ Γ(1 − ν+ ) √ A−X z 2 ν+ I−ν+ (z(A − X)). 21) 2. Let X1 ∈]0, A[ ﬁxed. Then, for k = 0, 1, the following asymptotics hold uniformly for X ∈ ]0, X1 [, when z → +∞, z real, +(k) f1 2−ν+ (X, λ, z) = (−1)k √ 2π × ez(A−X) − iλ κ+ κ+ a+ 1+O 1 z Γ(1 − ν+ ) z . 22) Vol. 12 (2011) Inverse Scattering in Black Holes 33 Proof. 20), observing that ( x2 )ν I−ν (x) is holomorphic on C. For the second one, let us recall the wellknown asymptotics for the modiﬁed Bessel function I−ν (x), ν ∈ C, k = 0, 1, when x → +∞: ex (k) (1 + O(|x|−1 )), x → +∞.