• Corpus ID: 235265729

A separation lemma on sub-lattices

@inproceedings{Wang2021ASL,
  title={A separation lemma on sub-lattices},
  author={W.-M. Wang},
  year={2021}
}
  • W. Wang
  • Published 1 June 2021
  • Mathematics
We prove that Bourgain’s separation lemma, Lemma 20.14 [B2] holds at fixed frequencies and their neighborhoods, on sub-lattices, sub-modules of the dual lattice associated with a quasi-periodic Fourier series in two dimensions. And by extension holds on the affine spaces. Previously Bourgain’s lemma was not deterministic, and is valid only for a set of frequencies of positive measure. The new separation lemma generalizes classical lattice partition-type results to the hyperbolic Lorentzian… 
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References

SHOWING 1-10 OF 11 REFERENCES
QUASI-PERIODIC SOLUTIONS OF HAMILTONIAN PERTURBATIONS OF 2D LINEAR SCHRODINGER EQUATIONS
The general problem discussed here is the persistency of quasi-periodic solutions of linear or integrable equations after Hamiltonian perturbation. This subject is closely related to the well-known
DENSITY OF POWER‐FREE VALUES OF POLYNOMIALS
We establish asymptotic formulae for the number of $k$-free values of polynmilas $F(x_1,\cdots,x_n)\in\mathbb{Z}[x_1,\cdots,x_n]$ of degree $d\geq 2$ for any $n\geq 1$, including when the variables
A KAM algorithm for the resonant non-linear Schrödinger equation
Abstract We prove, through a KAM algorithm, the existence of large families of stable and unstable quasi-periodic solutions for the NLS in any number of independent frequencies. The main tools are
Norm form equations I
Abstract We consider the general norm form equation over a function field. Under the usual condition, that the module in which the solutions lie be assumed non-degenerate, we prove that there are
Green's Function Estimates for Lattice Schrödinger Operators and Applications.
Acknowledgment v CHAPTER 1: Introduction 1 CHAPTER 2: Transfer Matrix and Lyapounov Exponent 11 CHAPTER 3: Herman's Subharmonicity Method 15 CHAPTER 4: Estimates on Subharmonic Functions 19 CHAPTER
Semi-algebraic sets method in PDE and mathematical physics
This paper surveys recent progress in the analysis of nonlinear partial differential equations using Anderson localization and semi-algebraic sets method. We discuss the application of these tools
A P ] 2 J un 2 02 1 QUASI-PERIODIC SOLUTIONS TO A NONLINEAR KLEIN-GORDON EQUATION WITH A DECAYING NONLINEAR TERM
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KAM for the nonlinear Schrödinger equation
We consider the $d$-dimensional nonlinear Schrodinger equation under periodic boundary conditions: $-i\dot u=-\Delta u+V(x)*u+\ep \frac{\p F}{\p \bar u}(x,u,\bar u), \quad u=u(t,x), x\in\T^d $ where
Energy supercritical nonlinear Schrödinger equations: Quasiperiodic solutions
We construct time quasi-periodic solutions to the energy supercritical nonlinear Schr\"odinger equations on the torus in arbitrary dimensions. This introduces a new approach, which could have general
Diophantine Approximations
Distribution Modulo One and Diophantine ApproximationDiophantine Approximation and the Geometry of Limit Sets in Gromov Hyperbolic Metric SpacesDiophantine GeometryCollected Mathematical Works:
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