The Shifted Harmonic Oscillator and the Hypoelliptic Laplacian on the Circle

Boris Mityagin, Petr Siegl, Joe Viola

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
JournalAnnales Henri Poincare
Early online date22 Apr 2021
DOIs
Publication statusEarly online date - 22 Apr 2021

Fingerprint

Dive into the research topics of 'The Shifted Harmonic Oscillator and the Hypoelliptic Laplacian on the Circle'. Together they form a unique fingerprint.

Cite this