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.References
- L. Gȧrding and B. Malgrange, Opérateurs différentiels partiellement hypoelliptiques et partiellement elliptiques, Math. Scand. 9 (1961), 5–21 (French). MR 126070, DOI 10.7146/math.scand.a-10619
- Takeshi Kotake and Mudumbai S. Narasimhan, Regularity theorems for fractional powers of a linear elliptic operator, Bull. Soc. Math. France 90 (1962), 449–471. MR 149329, DOI 10.24033/bsmf.1584
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