Author
Walter K. Hayman
Other affiliations: University of York
Bio: Walter K. Hayman is an academic researcher from Imperial College London. The author has contributed to research in topics: Meromorphic function & Power series. The author has an hindex of 20, co-authored 67 publications receiving 1948 citations. Previous affiliations of Walter K. Hayman include University of York.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the authors developed the theory initiated by Wiman [22, 23] and deepened by other writers including Valiron [18, 19, 20], Saxer [15], Clunie [4, 5] and Kovari [10, 11] which describes the local behaviour of f(z), near a point where | fz | is large, in terms of the power seriesf of f
Abstract: Suppose that 1.1 is a transcendental integral function. In this article we develop the theory initiated by Wiman [22, 23] and deepened by other writers including Valiron [18, 19, 20], Saxer [15], Clunie [4, 5] and Kovari [10, 11], which describes the local behaviour of f(z), near a point where | f(z) | is large, in terms of the power seriesf of f(z).
269 citations
222 citations
178 citations
111 citations
Cited by
More filters
TL;DR: In this paper, the authors describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions, and some aspects where the transcendental case is analogous to the rational case are treated rather briefly here.
Abstract: This paper attempts to describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions. The reader is not expected to be familiar with the iteration theory of rational functions. On the other hand, some aspects where the transcendental case is analogous to the rational case are treated rather briefly here. For example, we introduce the different types of components of the Fatou set that occur in the iteration of rational functions but omit a detailed description of these types. Instead, we concentrate on the types of components that are special to transcendental functions (Baker domains and wandering domains).
737 citations
TL;DR: The space of all Bloch functions will be denoted by «^. z€D'' as mentioned in this paper, which is equivalent to a well-known theorem of Bloch, and can be expressed in terms of the largest schlicht disc in the Riemann image surf ace.
Abstract: The space of all Bloch functions will be denoted by «^. There are several distinct characterisations of Bloch functions: (i) f € @l if and only if the f amily of functions f,(*) = ΐ(φ(*ϊ) f(?(0)); φ(ζ) = -ff^·, | a |< l, is finitely normal in D [28]. (ii) Let df(z) denote the largest schlicht disc around the point f(z) on the Riemann image surf ace by /. Then f € SS if and only if b = sup df(z) < oo. z€D This is equivalent to a well-known theorem of Bloch. In quantitative terms
439 citations
TL;DR: In this paper, a sharp quantitative version of the anisotropic isoperimetric inequality is established, corresponding to a stability estimate for the Wulff shape of a given surface tension energy.
Abstract: A sharp quantitative version of the anisotropic isoperimetric inequality is established, corresponding to a stability estimate for the Wulff shape of a given surface tension energy. This is achieved by exploiting mass transportation theory, especially Gromov’s proof of the isoperimetric inequality and the Brenier-McCann Theorem. A sharp quantitative version of the Brunn-Minkowski inequality for convex sets is proved as a corollary.
403 citations