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
Abstract: In this note we give a short proof of a theorem of Kotake and Narasimhan to the effect that if is a strongly elliptic operator of order with analytic coefficients and , where is some suitable norm, then is analytic. (Actually Kotake and Narasimhan prove the theorem when 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.
-  L. GÈ§rding and B. Malgrange, Opérateurs différentiels partiellement hypoelliptiques et partiellement elliptiques, Math. Scand. 9 (1961), 5–21 (French). MR 0126070, https://doi.org/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 0149329
- 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)
- 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)
Keywords: Elliptic operator, analytic function, conditionally elliptic operator
Article copyright: © Copyright 1971 American Mathematical Society