In this paper, we study the spectrum of the operator (Formula presented.) on L2(Rd/Г) with Γ a maximal dimension lattice in Rd and V a pseudodifferential operator of order strictly smaller than M. We prove that most of its eigenvalues admit the asymptotic expansion (Formula presented.) where Z is a C∞(Rd) function (symbol) and ξϵГ* (the dual lattice of Γ).
On the spectrum of the Schrödinger operator on Td: a normal form approach / D.P. BAMBUSI, B. LANGELLA, R. MONTALTO. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 45:4(2020 Apr 02), pp. 303-320.
On the spectrum of the Schrödinger operator on Td: a normal form approach
D.P. BAMBUSI
Primo
;B. LANGELLASecondo
;R. MONTALTOUltimo
2020
Abstract
In this paper, we study the spectrum of the operator (Formula presented.) on L2(Rd/Г) with Γ a maximal dimension lattice in Rd and V a pseudodifferential operator of order strictly smaller than M. We prove that most of its eigenvalues admit the asymptotic expansion (Formula presented.) where Z is a C∞(Rd) function (symbol) and ξϵГ* (the dual lattice of Γ).
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