On local and global analytic and Gevrey hypoellipticity

Michael Christ

Displaying similar documents to “On local and global analytic and Gevrey hypoellipticity”

Analytic hypoellipticity for sums of squares of vector fields

A. Alexandrou Himonas (1998)

Annales Polonici Mathematici

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We discuss the open problem of analytic hypoellipticity for sums of squares of vector fields, including some recent partial results and a conjecture of Treves.

Antilocality of complex powers of elliptic differential operators with analytic coefficients

Otto Liess (1982)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Failure of analytic hypoellipticity in a class of differential operators

Ovidiu Costin, Rodica D. Costin (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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For the hypoelliptic differential operators $P = \partial_{x}^{2} + {(x^{k} \partial_{y} - x^{l} \partial_{t})}^{2}$ introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of $k$ and $l$ left open in the analysis, the operators $P$ also fail to be analytic hypoelliptic (except for $(k, l) = (0, 1)$ ), in accordance with Treves’ conjecture. The proof is constructive, suitable for generalization, and relies on evaluating a family of eigenvalues of a non-self-adjoint operator.

Analytic and Gevrey Hypoellipticity

Luigi Rodino (1985)

Publications mathématiques et informatique de Rennes

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Analytic approximation for homogeneous solutions of linear PDE's

Mohamed S. Baouendi (1983)

Journées équations aux dérivées partielles

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Analytic functions in general analysis

Angus E. Taylor (1937)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Neighborhoods of a certain class of analytic functions with negative coefficients.

Cătaş, Adriana (2008)

Banach Journal of Mathematical Analysis [electronic only]

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Extendability of C. R. functions : a microlocal version of Bochner's tube theorem

Mohamed S. Baouendi (1981)

Journées équations aux dérivées partielles

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A note on composition operators on spaces of real analytic functions

Paweł Domański, Michał Goliński, Michael Langenbruch (2012)

Annales Polonici Mathematici

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We characterize composition operators on spaces of real analytic functions which are open onto their images. We give an example of a semiproper map φ such that the associated composition operator is not open onto its image.