@article{4ca3b637ab064161ad5a1a862cfe1cdf,
title = "The Shifted Harmonic Oscillator and the Hypoelliptic Laplacian on the Circle",
abstract = "We study the semigroup generated by the hypoelliptic Laplacian on the circle and the maximal bounded holomorphic extension of this semigroup. Using an orthogonal decomposition into harmonic oscillators with complex shifts, we describe the domain of this extension and we show that boundedness in a half plane corresponds to absolute convergence of the expansion of the semigroup in eigenfunctions. This relies on a novel integral formula for the spectral projections which also gives asymptotics for Laguerre polynomials in a large parameter regime.",
author = "Boris Mityagin and Petr Siegl and Joe Viola",
note = "Funding Information: The authors would like to thank the Institut Henri Poincar{\'e} for very pleasant working conditions during their stay in September 2018. The authors would also like to thank D. Zeilberger for helpful discussions. The third author gratefully acknowledges the support of the R{\'e}gion Pays de la Loire through the project EONE ({\'E}volution des Op{\'e}rateurs Non-Elliptiques). Funding Information: The authors would like to thank the Institut Henri Poincar? for very pleasant working conditions during their stay in September 2018. The authors would also like to thank D. Zeilberger for helpful discussions. The third author gratefully acknowledges the support of the R?gion Pays de la Loire through the project EONE (?volution des Op?rateurs Non-Elliptiques). Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.",
year = "2021",
month = oct,
doi = "10.1007/s00023-021-01053-0",
language = "English",
volume = "22",
pages = "3311--3355",
journal = "Annales Henri Poincare",
issn = "1424-0637",
publisher = "Birkh{\"a}user",
number = "10",
}