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Communications in Mathematical Physics - Volume 307 by M. Aizenman (Chief Editor)

By M. Aizenman (Chief Editor)

Articles during this volume:

On Majorana Representations of A6 and A7
A. A. Ivanov

Stability and Instability of maximum Reissner-Nordström Black gap Spacetimes for Linear Scalar Perturbations I
Stefanos Aretakis

Random Time-Dependent Quantum Walks
Alain Joye

Quantum Isometries of the Finite Noncommutative Geometry of the traditional Model
Jyotishman Bhowmick, Francesco D’Andrea and Ludwik Dąbrowski

Suitable recommendations for the Navier–Stokes challenge with an Homogeneous preliminary Value
Pierre Gilles Lemarié–Rieusset and Frédéric Lelièvre

Effective balance for Gevrey and Finitely Differentiable well-known Hamiltonians
Abed Bounemoura

One-Dimensional Chern-Simons Theory
Anton Alekseev and Pavel Mnëv

Parabolic shows of the large Yangian
Yung-Ning Peng

The Holst motion by way of the Spectral motion Principle
Frank Pfäffle and Christoph A. Stephan

Strongly targeted Gravitational Waves
Michael Reiterer and Eugene Trubowitz

Protecting the Conformal Symmetry through Bulk Renormalization on Anti deSitter Space
Michael Dütsch and Karl-Henning Rehren

Curvature Diffusions as a rule Relativity
Jacques Franchi and Yves Le Jan

KAM for the Quantum Harmonic Oscillator
Benoît Grébert and Laurent Thomann

Wall Crossing as noticeable by way of Matrix Models
Hirosi Ooguri, Piotr Sułkowski and Masahito Yamazaki

The Exoticness and Realisability of Twisted Haagerup–Izumi Modular Data
David E. Evans and Terry Gannon

Spectrum of Non-Hermitian Heavy Tailed Random Matrices
Charles Bordenave, Pietro Caputo and Djalil Chafaï

Erratum to: Diffusion on the Random Matrix tough Edge
José A. Ramírez and Brian Rider

Erratum to: Unitary Representations of tremendous Lie teams and purposes to the category and Multiplet constitution of great Particles
C. Carmeli, G. Cassinelli, A. Toigo and V. S. Varadarajan

Quantum delivery in Crystals: powerful Mass Theorem and K·P Hamiltonians
Luigi Barletti and Naoufel Ben Abdallah

A brief facts of balance of Topological Order less than neighborhood Perturbations
Sergey Bravyi and Matthew B. Hastings

A KAM Theorem for Hamiltonian Partial Differential Equations with Unbounded Perturbations
Jianjun Liu and Xiaoping Yuan

String buildings and Trivialisations of a Pfaffian Line Bundle
Ulrich Bunke

Global recommendations to the 3-D Incompressible Anisotropic Navier-Stokes method within the severe Spaces
Marius Paicu and Ping Zhang

Orthogonal and Symplectic Matrix types: Universality and different Properties
M. Shcherbina

From a Large-Deviations precept to the Wasserstein Gradient circulate: a brand new Micro-Macro Passage
Stefan Adams, Nicolas Dirr, Mark A. Peletier and Johannes Zimmer

LSI for Kawasaki Dynamics with susceptible Interaction
Georg Menz

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Extra resources for Communications in Mathematical Physics - Volume 307

Example text

The remaining local estimates are exactly the same. 12. 2) degenerates with respect to the transversal derivative ∂r to H+ . In order to remove this degeneracy we commute the wave equation g ψ = 0 with ∂r aiming at additionally controlling all the second derivatives of ψ (on the spacelike hypersurfaces and the spacetime region up to and including the horizon H+ ). Such commutations first appeared in [23]. 1. The spherically symmetric case. Let us first consider spherically symmetric waves. 1. 1) ∂r ψ + ψ M is conserved along H+ .

Aretakis 14. Uniform Pointwise Boundedness It remains to show that all solutions ψ of the wave equation are uniformly bounded. Proof of Theorem 4 of Sect. 4. We decompose ψ = ψ0 + ψ≥1 and prove that each projection is uniformly bounded by a norm that depends only on initial data. Indeed, by applying the following Sobolev inequality on the hypersurfaces τ we have ψ≥1 L∞( τ) ψ≥1 ≤C . 1 H ( τ) + ψ≥1 . 1) where C depends only on 0 . Note also that we use the Sobolev inequality that does not involve the L 2 -norms of zeroth order terms.

Recall that the eigenvalues of the spherical Laplacian / are equal to −l(l+1) r2 l The dimension of the eigenspaces E is equal to 2l + 1 and the corresponding eigenvectors are denoted by Y m,l , −l ≤ m ≤ l and called spherical harmonics. We have L 2 (S2 (r )) = ⊕l≥0 E l and, therefore, any function ψ ∈ L 2 (S2 (r )) can be written as ∞ l ψm,l Y m,l . 1) Linear Stability and Instability of Extreme Reissner-Nordström I 33 The right-hand side converges to ψ in L 2 of the spheres and under stronger regularity assumptions the convergence is pointwise.

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