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- W2316205963 abstract "Let D be the unit disk in the complex plane. Let p ( z , z ’) denote the hyperbolic distance between z and z’ in ((1 + u)/ (1 — u)) = tanh -1 u, [ 6 , chapter 15]). Let W be the Riemann sphere with the chordal metric. A complex valued function F (Z) in D is a normal function if lor each pair of sequences {z n } and {z n ’} of points in D such that the convergence of {(fz n )} to a value α in W implies the convergence of {f(z n ’)} to α. Two sequences {z n } and {z n ’} of points in D are called close sequences if ρ(z n , z n ’) → 0. (There are several equivalent definitions of normality if the functions are meromorphic.) The definition of a normal function implies that a normal function is continuous at each point of D when using the Euclidean metric in the domain and the chordal metric in the range. We wish to study the sums and products of normal functions. Some functions, such as a function in a Hardy p -class, p > 0, (or really any function of bounded characteristic) can be written as a sum or product of two normal functions, but sums and products of normal functions need not be normal (see Lappan [7])." @default.
- W2316205963 created "2016-06-24" @default.
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- W2316205963 date "1972-04-01" @default.
- W2316205963 modified "2023-10-14" @default.
- W2316205963 title "Sums and Products of Normal Functions" @default.
- W2316205963 doi "https://doi.org/10.4153/cjm-1972-020-3" @default.
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