Displaying similar documents to “The four positive vortices problem : regions of chaotic behavior and the non-integrability”

The phase of the Daubechies filters.

Djalil Kateb, Pierre Gilles Lemarié-Rieusset (1997)

Revista Matemática Iberoamericana

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We give the first term of the asymptotic development for the phase of the N-th (minimum-phased) Daubechies filter as N goes to +∞. We obtain this result through the description of the complex zeros of the associated polynomial of degree 2N+1.

Norm estimates of discrete Schrödinger operators

Ryszard Szwarc (1998)

Colloquium Mathematicae

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Harper’s operator is defined on ℓ 2 ( Z ) by H θ ξ ( n ) = ξ ( n + 1 ) + ξ ( n - 1 ) + 2 cos n θ ξ ( n ) , where θ ∈ [ 0 , π ] . We show that the norm of ∥ H θ ∥ is less than or equal to 2 2 for π / 2 ≤ θ ≤ π . This solves a conjecture stated in [1]. A general formula for estimating the norm of self-adjoint tridiagonal infinite matrices is also derived.