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Concentration of Eigenfunctions of Schrödinger Operators

Autor: Boris Mityagin, Petr Siegl, Joe Viola

Publikováno v: Journal of Fourier Analysis and Applications. 28

We consider the limit measures induced by the rescaled eigenfunctions of Schrödinger operators with even confining potentials. We show that the limit measure is supported on $$[-1,1]$$ [ - 1 , 1 ] and with the density proportional to $$(1-|x|^\beta

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::eacb84ec494c584cf41d09fef198563a
https://doi.org/10.1007/s00041-022-09961-3

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Akademický článek

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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

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Akademický článek

Berklee pays tribute to saxophone master Joe Viola.

Publikováno v: American Music Teacher. Aug/Sep97, Vol. 47 Issue 1, p4. 2/9p. 1 Black and White Photograph.

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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

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The shifted harmonic oscillator and the hypoelliptic Laplacian on the circle

Autor: Joe Viola, Petr Siegl, Boris Mityagin

Publikováno v: Mityagin, B, Siegl, P & Viola, J 2021, ' The Shifted Harmonic Oscillator and the Hypoelliptic Laplacian on the Circle ', Annales Henri Poincare . https://doi.org/10.1007/s00023-021-01053-0

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 t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a5be7455003f025220691affc812f44d

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Applications of a metaplectic calculus to Schrödinger evolutions with non-self-adjoint generators

Autor: Joe Viola

Publikováno v: Journées Équations aux Dérivées Partielles
Journées Équations aux Dérivées Partielles, Jun 2018, Obernai, France. pp.1-11, ⟨10.5802/jedp.671⟩

International audience; Applications of a metaplectic calculus to Schrödinger evolutions with non-self-adjoint generators Abstract We review the calculus of metaplectic operators and shifts in phase space applied to Gaussian wave packets. Using holo

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::483e886ba797abac871bc097fea5c0ff
https://hal.archives-ouvertes.fr/hal-02493836/document

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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

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Singular-Value Decomposition of Solution Operators to Model Evolution Equations: Fig. 1

Autor: Alexandru Aleman, Joe Viola

Publikováno v: International Mathematics Research Notices. 2015:8275-8288

We consider evolution equations generated by quadratic operators admitting a decomposition in creation-annihilation operators without usual ellipticity-type hypotheses; this class includes hypocoercive model operators. We identify the singular-value

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::3d7ba2c2b3cdf8c2f31b763373766ffe
https://doi.org/10.1093/imrn/rnu199

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