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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Analytic properties of elliptic and conditionally elliptic operators.

Author: Michael E. Taylor
Journal: Proc. Amer. Math. Soc. 28 (1971), 317-318
MSC: Primary 35.43; Secondary 46.00
MathSciNet review: 0276609
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Abstract: In this note we give a short proof of a theorem of Kotake and Narasimhan to the effect that if $ A$ is a strongly elliptic operator of order $ 2m$ with analytic coefficients and $ \vert\vert{A^j}u\vert\vert \leqq {C^{j + 1}}(2mj)!$, where $ \vert\vert\;\vert\vert$ is some suitable norm, then $ u$ is analytic. (Actually Kotake and Narasimhan prove the theorem when $ A$ is elliptic, but the trick we use here requires some specialization.) This is applied to derive a short proof of a theorem proved by Gårding and Malgrange, in the constant coefficients case, concerning conditionally elliptic operators.

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  • [1] L. Gårding and B. Malgrange, Opérateurs différentiels partiellement hypoelliptiques et partiellement elliptiques, Math. Scand. 9 (1961), 5-21. MR 23 #A3367. MR 0126070 (23:A3367)
  • [2] T. Kotake and M. S. Narasimhan, Regularity theorems for fractional powers of linear elliptic operators, Bull. Soc. Math. France 90 (1962), 449-471. MR 26 #6819. MR 0149329 (26:6819)

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Keywords: Elliptic operator, analytic function, conditionally elliptic operator
Article copyright: © Copyright 1971 American Mathematical Society

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