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 thought: Wigner Matrices, 3j Symbols, and personality Localization
Joseph Ben Geloun and Razvan Gurau

Spectral research of a good 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 measurement 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 varieties for Theories with Gauge team 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 thought 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 concept for Multimodal Maps
Godofredo Iommi and Mike Todd

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

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

Coulomb platforms 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 conception at the Noncommutative Two-Dimensional Minkowski house with Grosse–Wulkenhaar Potential
Jochen Zahn

Ground kingdom Representations of Loop Algebras
Yoh Tanimoto

The 1/N growth of coloured Tensor Models
Razvan Gurau

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

A classification 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 strains 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 facet Currents alongside Magnetic boundaries and Magnetic Guides
Nicolas Dombrowski, François Germinet and Georgi Raikov

From confident box conception 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 floor country power of the Massless Spin-Boson Model
Abdelmalek Abdesselam

Resolvent Estimates for in most cases 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 thought for a Mathematical version of the susceptible 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 power 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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Extra info for Annales Henri Poincaré - Volume 12

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However, this is not the case. This is an important point, which makes the system of Eqs. (1)–(2) very peculiar. The reason is the following. The elliptic equation (2) can be solved, for a given function v, using a Green function. We can insert the solution β into Eq. (1) to reduce the system to only one integro-differential equation for v. It is a priori not clear at all how to solve this integro-differential equation due to the singular behavior at the axis. If we take an integral transform to the system, we get also an integro-differential equation in momentum space (see Eq.

We apply the Hankel transform to Eq. (34) and we obtain the following equation in momentum space ¨ ˆ k) + H(T (γ)). w(t, ˆ k) = −(1 + k 2 )w(t, (63) Using the expression for H(T (γ)) obtained in Lemma 2 we obtain ∞ 3 ¨ ˆ k) − w(t, ˆ k) = −(1 + k 2 )w(t, 2k 2 1 (1 + k 2 ) 2 k 1 (1 + k¯2 ) 2 ¯ dk. ¯ w(t, ˆ k) 1 k¯ 2 (64) This equation involves only w, ˆ and hence we have reduced the system (34)– (35) to only one equation for one unknown. But Eq. (64) is not a differential equation, it is an integro-differential equation.

But in any case, even without such characterization, it clear that for this kind of operators (namely, derivatives with respect to ρ times some power of ρ) it possible to compute the Hankel transform in some way. From these considerations, it would appear that an analog of Theorem 1 will hold for a whole family of similar equations. However, this is not the case. This is an important point, which makes the system of Eqs. (1)–(2) very peculiar. The reason is the following. The elliptic equation (2) can be solved, for a given function v, using a Green function.

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