Duke Mathematical Journal

Complete asymptotic expansion of the spectral function of multidimensional almost-periodic Schrödinger operators

Leonid Parnovski and Roman Shterenberg

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Abstract

We prove the existence of a complete asymptotic expansion of the spectral function (the integral kernel of the spectral projection) of a Schrödinger operator H=Δ+b acting in Rd when the potential b is real and either smooth periodic, or generic quasiperiodic (finite linear combination of exponentials), or belongs to a wide class of almost-periodic functions.

Article information

Source
Duke Math. J., Volume 165, Number 3 (2016), 509-561.

Dates
Received: 24 June 2014
Revised: 20 March 2015
First available in Project Euclid: 17 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1450389253

Digital Object Identifier
doi:10.1215/00127094-3166415

Mathematical Reviews number (MathSciNet)
MR3466162

Zentralblatt MATH identifier
1337.35104

Subjects
Primary: 35P20: Asymptotic distribution of eigenvalues and eigenfunctions
Secondary: 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis 47G30: Pseudodifferential operators [See also 35Sxx, 58Jxx] 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]

Keywords
periodic operators almost-periodic pseudodifferential operators spectral function

Citation

Parnovski, Leonid; Shterenberg, Roman. Complete asymptotic expansion of the spectral function of multidimensional almost-periodic Schrödinger operators. Duke Math. J. 165 (2016), no. 3, 509--561. doi:10.1215/00127094-3166415. https://projecteuclid.org/euclid.dmj/1450389253


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