Consider the one-dimensional discrete Schrödinger operator Hθ: (Hθq)n=−(qn+1+qn−1)+V(θ+nω)qn,n∈Z, with ω∈Rd Diophantine, and V a real-analytic function on Td=(R/2πZ)d. For V sufficiently small, we prove the dispersive estimate: for every ϕ∈ℓ1(Z), ‖e−itHjavax.xml.bind.JAXBElement@451f543ϕ‖ℓjavax.xml.bind.JAXBElement@31c1caec≤K0[Formula presented]‖ϕ‖ℓjavax.xml.bind.JAXBElement@6e0bf990,〈t〉:=1+t2, with a and K0 two absolute constants and ε0 an analytic norm of V. The estimate holds for every θ∈Td.
Dispersive estimate for quasi-periodic Schrödinger operators on 1-d lattices / D. Bambusi, Z. Zhao. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 366:(2020 Jun 03). [10.1016/j.aim.2020.107071]
Dispersive estimate for quasi-periodic Schrödinger operators on 1-d lattices
D. Bambusi
Primo
;
2020
Abstract
Consider the one-dimensional discrete Schrödinger operator Hθ: (Hθq)n=−(qn+1+qn−1)+V(θ+nω)qn,n∈Z, with ω∈Rd Diophantine, and V a real-analytic function on Td=(R/2πZ)d. For V sufficiently small, we prove the dispersive estimate: for every ϕ∈ℓ1(Z), ‖e−itHjavax.xml.bind.JAXBElement@451f543ϕ‖ℓjavax.xml.bind.JAXBElement@31c1caec≤K0[Formula presented]‖ϕ‖ℓjavax.xml.bind.JAXBElement@6e0bf990,〈t〉:=1+t2, with a and K0 two absolute constants and ε0 an analytic norm of V. The estimate holds for every θ∈Td.File | Dimensione | Formato | |
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