An Application of the Analytic Microlocal Analysis to a Class of Differential Operators of Mixed Type

✍ Scribed by T. V. Gramchev

• Publisher: John Wiley and Sons
• Year: 1985
• Tongue: English
• Weight: 408 KB
• Volume: 121
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19851210106

✦ Synopsis

51. Some Preliminaries and Statement of the Results

The main purpose of this article is to apply some results from the analytic microlocal analysis [6], [ll], [13] for study of analytic singularities for a class of differential operators of mixed type. In the announcement [4] the author considered the homogeneous Tricomi operator 2.02, + DZ3.

Let P(x, D), x E R" be a differential operator of order m, with analytic coefficients and real principal symbol p ( x , E), such that

Under this assumption in [l], [6] it was proved that for each distribution U ( Z ) E D'(Rn), WF,u \ WF,Pu is invariant under the Hamilton flow ITp (i.e. the analytic singularities propagate along the bicharacteristics of p ) . In this paper we investigate differential operators, of second order, for which (1.1) is not satisfied everywhere, but d,p(x, E ) + 0 assoonasdtp(x, l ) = 0, 5 + 0.