Analytic properties of elliptic and conditionally elliptic operators.
Michael E. Taylor
Proc. Amer. Math. Soc. 28 (1971), 317-318
Primary 35.43; Secondary 46.00
Full-text PDF Free Access
Similar Articles |
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. 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)
Retrieve articles in Proceedings of the American Mathematical Society
Retrieve articles in all journals
conditionally elliptic operator
© Copyright 1971 American Mathematical Society