@article{0280b78ead2449f0ba2e3b4469902922,
title = "Differential operators admitting various rates of spectral projection growth",
abstract = "We consider families of non-self-adjoint perturbations of self-adjoint Schr{\"o}dinger operators with single-well potentials. The norms of spectral projections of these operators are found to grow at intermediate rates from arbitrarily slowly to exponentially rapidly.",
keywords = "Harmonic and anharmonic oscillators, Hermite functions, Riesz basis, Spectral projections",
author = "Boris Mityagin and Petr Siegl and Joe Viola",
note = "Funding Information: P. S. acknowledges the support of SCIEX-NMS Fellowship 11.263 and SNF Ambizione project PZ00P2_154786. J. V. is grateful for the support of ANR NOSEVOL (Project number: ANR 2011 BS01019 01). The authors acknowledge the very pleasant working conditions at the ICMS Workshop Mathematical aspects of the physics with non-self-adjoint operators, held in March 2013 in Edinburgh, UK, during which this work was initiated. The authors would also like to thank Andrei Mart{\`i}nez–Finkelshtein for very valuable advice on references and calculations in Proposition 4.1, Section 4. The authors would like to thank Rapha{\"e}l Henry for bringing an important concern to our attention. Finally, the authors would like to express their gratitude to the anonymous referee for a careful reading and many helpful suggestions. Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",
year = "2017",
month = apr,
day = "15",
doi = "10.1016/j.jfa.2016.12.007",
language = "English",
volume = "272",
pages = "3129--3175",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press",
number = "8",
}