Lateral estimates for iterated elliptic operators and analyticity.

Tarama, Shigeo

Displaying similar documents to “Lateral estimates for iterated elliptic operators and analyticity.”

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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Regularity theorems for fractional powers of a linear elliptic operator

Takeshi Kotake, Mudumbai S. Narasimhan (1962)

Bulletin de la Société Mathématique de France

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Generation of analytic semigroups by elliptic operators of second order in Hölder spaces

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Two Estimates for Integral Means of Analytic Functions in the Unit Disc

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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 continuation for some classes of separately analytic functions of real variables

Nguyen Thanh Van (2003)

Annales Polonici Mathematici

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For functions that are separately solutions of an elliptic homogeneous PDE with constant coefficients, we prove an analogue of Siciak's theorem for separately holomorphic functions.

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.