Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
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Let C=(C"n)"n"@?"N and D=(D^n)"n"@?"N be families of composition and differentiation operators, respectively, i.e., C"nf=f@?@f"n,Df=f^', where f is holomorphic on some domain @W@?C. Our main question is: How fast can a totally bounded set M of holomorphic functions, in other words a normal family, be approximated by the ''orbit'' {C"nf:n@?N} or {D^nf:n@?N}, respectively, of one suitably constructed function f? Our answer consists of upper bounds for the numbers F(f,1/n):=inf{N@?N:Any g@?M is approximable with error