The shifted harmonic oscillator and the hypoelliptic Laplacian on the circle
Spectral Theory
2021-09-29 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.2011.12027,
title = {The shifted harmonic oscillator and the hypoelliptic Laplacian on the circle},
author = {Boris Mityagin and Petr Siegl and Joe Viola},
journal= {arXiv preprint arXiv:2011.12027},
year = {2021}
}
Comments
40 pages, 3 figures