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Transformations of domains in the plane and applications in the theory of functions

1964
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Pacific Journal of Mathematics
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In this paper we shall consider a family of transformations S n (n = 1, 2, •) operating on open or closed sets in the complex plane s S n is defined relatively to a fixed point called the center of transformation, and it transforms an open set into a starlike domain which, for n > 1, is also %-fold symmetric with respect to this point. Therefore, for n > 1, S n may be classified as a method of symmetrization. This method of symmetrization was already defined by Szego [4] for domains which are

doi:10.2140/pjm.1964.14.613
fatcat:qrh7g2sbtzcrzeqwcfc32yteem