Nonlinear eigenvalues and analytic hypoellipticity

Sagun Chanillo; Bernard Helffer; Ari Laptev

doi:10.1016/S0022-1236(03)00105-8

Nonlinear eigenvalues and analytic hypoellipticity

Sagun Chanillo, Bernard Helffer, Ari Laptev

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

Motivated by the problem of analytic hypoellipticity, we show that a special family of compact non-self-adjoint operators has a nonzero eigenvalue. We recover old results obtained by ordinary differential equations techniques and show how it can be applied to the higher dimensional case. This gives in particular a new class of hypoelliptic, but not analytic hypoelliptic operators.

Original language	English (US)
Pages (from-to)	425-443
Number of pages	19
Journal	Journal of Functional Analysis
Volume	209
Issue number	2
DOIs	https://doi.org/10.1016/S0022-1236(03)00105-8
State	Published - Apr 15 2004

All Science Journal Classification (ASJC) codes

Analysis

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10.1016/S0022-1236(03)00105-8

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title = "Nonlinear eigenvalues and analytic hypoellipticity",

abstract = "Motivated by the problem of analytic hypoellipticity, we show that a special family of compact non-self-adjoint operators has a nonzero eigenvalue. We recover old results obtained by ordinary differential equations techniques and show how it can be applied to the higher dimensional case. This gives in particular a new class of hypoelliptic, but not analytic hypoelliptic operators.",

author = "Sagun Chanillo and Bernard Helffer and Ari Laptev",

note = "Funding Information: We thank A.S. Markus, D. Robert and M. Solomyak for useful correspondence. S.C. wishes to thank F. Tr{\`e}ves for his encouragement and Shri S. Devananda for useful comments. B.H. and A.L. thank the Mittag–Leffler Institute and a partial support by the SPECT ESF European programme. The research of S.C. was supported in part by a Grant from the NSF.",

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T1 - Nonlinear eigenvalues and analytic hypoellipticity

AU - Chanillo, Sagun

AU - Helffer, Bernard

AU - Laptev, Ari

N1 - Funding Information: We thank A.S. Markus, D. Robert and M. Solomyak for useful correspondence. S.C. wishes to thank F. Trèves for his encouragement and Shri S. Devananda for useful comments. B.H. and A.L. thank the Mittag–Leffler Institute and a partial support by the SPECT ESF European programme. The research of S.C. was supported in part by a Grant from the NSF.

PY - 2004/4/15

Y1 - 2004/4/15

N2 - Motivated by the problem of analytic hypoellipticity, we show that a special family of compact non-self-adjoint operators has a nonzero eigenvalue. We recover old results obtained by ordinary differential equations techniques and show how it can be applied to the higher dimensional case. This gives in particular a new class of hypoelliptic, but not analytic hypoelliptic operators.

AB - Motivated by the problem of analytic hypoellipticity, we show that a special family of compact non-self-adjoint operators has a nonzero eigenvalue. We recover old results obtained by ordinary differential equations techniques and show how it can be applied to the higher dimensional case. This gives in particular a new class of hypoelliptic, but not analytic hypoelliptic operators.

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DO - 10.1016/S0022-1236(03)00105-8

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VL - 209

SP - 425

EP - 443

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Nonlinear eigenvalues and analytic hypoellipticity

Abstract

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