Annales Henri Poincaré - Volume 12 by Vincent Rivasseau (Chief Editor)

By Vincent Rivasseau (Chief Editor)

Articles during this volume:

Inverse Scattering at fastened strength in de Sitter–Reissner–Nordström Black Holes
Thierry Daudé and François Nicoleau

Linear Perturbations for the Vacuum Axisymmetric Einstein Equations
Sergio Dain and Martín Reiris

A Volumetric Penrose Inequality for Conformally Flat Manifolds
Fernando Schwartz

Asymptotes in SU(2) Recoupling idea: Wigner Matrices, 3j Symbols, and personality Localization
Joseph Ben Geloun and Razvan Gurau

Spectral research of an efficient Hamiltonian in Nonrelativistic Quantum Electrodynamics
Asao Arai

Uniform Convergence of Schrödinger Cocycles over basic Toeplitz Subshift
Qing-Hui Liu and Yan-Hui Qu

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

On Breakdown standards for Nonvacuum Einstein Equations
Arick Shao

Further regulations at the Topology of desk bound Black Holes in 5 Dimensions
Stefan Hollands, Jan Holland and Akihiro Ishibashi

Fermi Coordinates, Simultaneity, and increasing house in Robertson–Walker Cosmologies
David Klein and Evan Randles

Existence of Dyons within the Coupled Georgi–Glashow–Skyrme Model
Fanghua Lin and Yisong Yang

Gauge Orbit kinds for Theories with Gauge staff O(n), SO(n) or Sp(n)
Alexander Hertsch, Gerd Rudolph and Matthias Schmidt

Exactly Solvable Schrödinger Operators
Jan Dereziński and Michał Wrochna

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

Topological Graph Polynomial and Quantum box conception half II: Mehler Kernel Theories
Thomas Krajewski, Vincent Rivasseau and Fabien Vignes-Tourneret

Homogeneous Schrödinger Operators on Half-Line
Laurent Bruneau, Jan Dereziński and Vladimir Georgescu

Dimension conception for Multimodal Maps
Godofredo Iommi and Mike Todd

Ground States within the Spin Boson Model
David Hasler and Ira Herbst

Aharonov–Bohm influence in Resonances of Magnetic Schrödinger Operators with Potentials with helps at huge Separation
Ivana Alexandrova and Hideo Tamura

Coulomb structures on Riemannian Manifolds and balance of Matter
Alberto Enciso

Random stroll on Surfaces with Hyperbolic Cusps
Hans Christianson, Colin Guillarmou and Laurent Michel

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

Ground nation Representations of Loop Algebras
Yoh Tanimoto

The 1/N enlargement of coloured Tensor Models
Razvan Gurau

Future balance of the Einstein-Maxwell-Scalar box System
Christopher Svedberg

A type of Dust-Like Self-Similar options of the Massless Einstein–Vlasov System
Alan D. Rendall and Juan J. L. Velázquez

Areas and Volumes for Null Cones
James D. E. Grant

Critical issues of Wang–Yau Quasi-Local Energy
Pengzi Miao, Luen-Fai Tam and Naqing Xie

Yamabe Numbers and the Brill–Cantor Criterion
Helmut Friedrich

On the Geometry of the Nodal traces of Eigenfunctions of the Two-Dimensional Torus
Jean Bourgain and Zeév Rudnick

Thermal results in Gravitational Hartree Systems
Gonca L. Aki, Jean Dolbeault and Christof Sparber

Lyapunov Exponents, Periodic Orbits and Horseshoes for Mappings of Hilbert Spaces
Zeng Lian and Lai-Sang Young

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

Associativity of box Algebras
Namhoon Kim

Quantization of aspect Currents alongside Magnetic limitations and Magnetic Guides
Nicolas Dombrowski, François Germinet and Georgi Raikov

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

Quantum Diffusion and Delocalization for Band Matrices with normal Distribution
László Erdős and Antti Knowles

The flooring nation strength of the Massless Spin-Boson Model
Abdelmalek Abdesselam

Resolvent Estimates for more often than not Hyperbolic Trapped Sets
Jared Wunsch and Maciej Zworski

Spacelike Localization of Long-Range Fields in a version of Asymptotic Electrodynamics
Andrzej Herdegen and Katarzyna Rejzner

Kochen–Specker units and Generalized Orthoarguesian Equations
Norman D. Megill and Mladen Pavičić

Recursion among Mumford Volumes of Moduli Spaces
Bertrand Eynard

Approximate KMS States for Scalar and Spinor Fields in Friedmann–Robertson–Walker Spacetimes
Claudio Dappiaggi, Thomas-Paul Hack and Nicola Pinamonti

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

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

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

Stochastic Description of a Bose–Einstein Condensate
Laura M. Morato and Stefania Ugolini

Semiclassical Propagation of Coherent States for the Hartree Equation
Agissilaos Athanassoulis, Thierry Paul, Federica Pezzotti and Mario Pulvirenti

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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 → +∞.

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