----------------------------------------------------- page 4 last line: ... neither elliptic nor hyperbolic ^^^^^^^^^^ page 12 equation (4): d theta, not dt page 12, 4 lines from bottom: ||b|| <= ||b||_infinity (not the other way around). page 31 line 6 (just after displayed equation). The limit statement should refer to: f_r composed with phi, ^^^ ^^^^^^^^ ^^^^ ^^^ not just to f_r. page 34 Problem 7, part (a), second line: if and only if \nu(f_n) page 35 four lines from bottom: "Hunziger", not "Huniziger" page 40, second line of large display: f_n'(\phi(z)) not f_n(\phi(z)) (the derivative symbol is missing) page 48 last line: \Psi_{\alpha,0,b}(\Pi) instead of \psi_{\alpha,0,b}(\pi) (Capital \psi and \pi instead of lower-case) page 55 eight lines from the bottom: delete the second hyphen in "Julia-Carathe'odory". page 57 last line of statement of Julia-Carath. Theorem: ``.. omegabar eta.." not "omega etabar" page 67 second line: "w_0 \in \Pi" (not "\omega_0 \in \Pi"). ^^^^^ four lines from bottom: "p \in \Pi" (not \phi \in \Pi). ^^^ page 71 in statement of Corollary: phi is a univalent self-map of U ^^^^^^^^^ (not just a holomorphic one: the Cor. is false for arbitrary self-maps, as I go to great lengths to show in Chapter 10.) page 74 Exercise 12: in second line: "boundary of U" not just "U" in third line: sup_n|\phi_n'(\zeta)| (subscript "n" is missing) page 98, Displayed statement in next-to-last paragraph: "If phi is a univalent self-map ..." ^^^ page 103, Exercise 12, part (a): Show that if T is compact, ^^^^^^^^^^^^^^^ then the diagonal entries of the matrix are the only eigenvalues of T. (The Backward Shift on H^2 is a counterexample to the result of part (a) as it is stated.) page 110 two lines after first display: The word "define" occurs twice. Delete one! page 196 Middle of page, two lines below displayed formula: " ... u=|f|^2 ..." not "... u = |f'|^2 .." page 178 second line before the Littlewood-Paley Identity: "... it is more convenient to put a little more care ..." ^^ page 189 next-to-last line of large display: Instead of ||z||^2 there should appear ||\phi||^2 - |\phi(0)|^2 which results from the integral of N_\phi that occurs in the line above upon appplying the change-of-variable formula (4) on p 179 to the function f(z) = z. page 190 right-hand side of inequality (22): Integrate with respect to dA(z), not dA(w). ^^^^^ page 200 third line before last paragraph:"Mascioni", not "Maschioni". page 208 references [KrM '90] and [KrM '92]: "Kriete", not" Kreite".(same error on index entry, page 218) page 211 reference [STa '72] IUMJ 23 (1973) ^^ (vol. 23, not vol. 125) page 212 reference [Sk1 '87] Composition semigroups ^^^^^^^^^^ (not Composition operators) ^^^^^^^^^ **************** In addition, I've been informed of these errors that I haven't checked yet: page 49 fourth line from top: y = Ax + Bx^\gamma (not y = A + Bx^\gamma) page 139 In the estimates involving w_{n+1} - w_n, one should not take the specific constants claimed there too seriously! **************** I'd like to thank Mihaela Poplicher, Maria Tjani, John Clifford, Aristomenis Siskakis, P. Galanopoulos, and Raymond Mortini for their help here. The latest corrections are available by anonymous ftp from: math.msu.edu in the file: pub/papers/shapiro Please let me know about any other mistakes you might encounter. ... Joel Shapiro (shapiro@math.msu.edu)