8. (Liouville's theorem, Cauchy estimates and the maximum modulus principle) (a) Suppose that f is entire, and that for some positive integer k and some constants C,r > 0 it holds that IS(2)|

Extracted text: 8. (Liouville's theorem, Cauchy estimates and the maximum modulus principle) (a) Suppose that f is entire, and that for some positive integer k and some constants C,r > 0 it holds that IS(2)| < c|zl*,="" |="|2r." show="" that="" f="" is="" a="" polynomial="" of="" degree="" at="" most="" k.="" (b)="" let="" f="" and="" g="" be="" analytic="" in="" |2|="">< 1.="" suppose="" also="" that="" they="" have="" no="" zeros="" there,="" and="" that="" is(:)|="\g(2)|" on="" |z|="1." show="" that="" there="" is="" a="" constant="" a="" with="" |a|="1" such="" that="" f(2)="">