The Shifted Harmonic Oscillator and the Hypoelliptic Laplacian on the Circle

Boris Mityagin, Petr Siegl, Joe Viola*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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
Pages (from-to)3311-3355
Number of pages45
JournalAnnales Henri Poincare
Issue number10
Publication statusPublished - Oct 2021
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics


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