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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Analytic properties of elliptic and conditionally elliptic operators.
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by Michael E. Taylor PDF
Proc. Amer. Math. Soc. 28 (1971), 317-318 Request permission

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 $||{A^j}u|| \leqq {C^{j + 1}}(2mj)!$, where $||\;||$ 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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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 28 (1971), 317-318
  • MSC: Primary 35.43; Secondary 46.00
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0276609-7
  • MathSciNet review: 0276609