Problem 1 ( Stein's Real Analysis , p. 257, # 18 ). Consider the linear partial differential operator* [ = > adam . lal En. of order ~ , whose characteristic polynomial is P ( 5 ) = >` ad ( 2 Tris ) a lalEn Recall that I is said to be elliptic if IP ( S)1 2 c/El" for some c > O and all & sufficiently large . ( a ) Check that I is elliptic if and only if the principal characteristic polyno - mial Pn ( 5 ) = > da ( 2 1is ) a lal = n of [ vanishes only when $ = 0 . ( b ) If I is elliptic , prove that for some c > O the inequality* 1/2 `1\\ [ 2 ( Red )