Quaternionic structure and analysis of some Kramers–Fokker–Planck operators

Autor: Mona Ben Said, Francis Nier, Joe Viola

Publikováno v: Asymptotic Analysis. 119:87-116

The present article is concerned with global subelliptic estimates for Kramers-Fokker-Planck operators with polynomials of degree less than or equal to two. The constants appearing in those estimates are accurately formulated in terms of the coeffici

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::49828418421bfc091ecbc7d7c01929a0
https://doi.org/10.3233/asy-191569

Short-time asymptotics of the regularizing effect for semigroups generated by quadratic operators

Autor: Karel Pravda-Starov, Joe Viola, Michael Hitrik

Publikováno v: Bulletin des Sciences Mathématiques
Bulletin des Sciences Mathématiques, Elsevier, 2017, 141 (7), pp.615-675. 〈10.1016/j.bulsci.2017.07.003〉
Bulletin des Sciences Mathématiques, Elsevier, 2017, 141 (7), pp.615-675. ⟨10.1016/j.bulsci.2017.07.003⟩
Bulletin des Sciences Mathématiques, 2017, 141 (7), pp.615-675. ⟨10.1016/j.bulsci.2017.07.003⟩

We study accretive quadratic operators with zero singular spaces. These degenerate non-selfadjoint differential operators are known to be hypoelliptic and to generate contraction semigroups which are smoothing in the Schwartz space for any positive t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::34b84fa280730dc4767359a1040b3dfd
https://doi.org/10.1016/j.bulsci.2017.07.003

From semigroups to subelliptic estimates for quadratic operators

Autor: Karel Pravda-Starov, Joe Viola, Michael Hitrik

Publikováno v: Transactions of the American Mathematical Society
Transactions of the American Mathematical Society, American Mathematical Society, 2018, 370 (10), pp.7391-7415. ⟨10.1090/tran/7251⟩
Transactions of the American Mathematical Society, American Mathematical Society, In press
Transactions of the American Mathematical Society, 2018, 370 (10), pp.7391-7415. ⟨10.1090/tran/7251⟩

Using an approach based on the techniques of FBI transforms, we give a new simple proof of the global subelliptic estimates for non-self-adjoint nonelliptic quadratic differential operators, under a natural averaging condition on the Weyl symbols of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1e89d3e5cdaec41c3ea77093e9577018
https://hal.archives-ouvertes.fr/hal-01219682

Non-Elliptic Quadratic Forms and Semiclassical Estimates for Non-selfadjoint Operators

Autor: Joe Viola

Publikováno v: International Mathematics Research Notices. 2013:4615-4671

We consider a class of pseudodifferential operators with a doubly characteristic point, where the quadratic part of the symbol fails to be elliptic but obeys an averaging assumption. Under suitable additional assumptions, semiclassical resolvent esti

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f46c64e5e0d446382b6c11cd1d72127d
https://doi.org/10.1093/imrn/rns188

On weak and strong solution operators for evolution equations coming from quadratic operators

Autor: Alexandru Aleman, Joe Viola

Publikováno v: Journal of Spectral Theory
Journal of Spectral Theory, European Mathematical Society, 2018, 8 (1), pp.33-121. ⟨10.4171/JST/191⟩

We identify, through a change of variables, solution operators for evolution equations with generators given by certain simple first-order differential operators acting on Fock spaces. This analysis applies, through unitary equivalence, to a broad cl

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::77f8d1853f11ffe012fd84fac743193f