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Bulletin of the London Mathematical Society 2001 33(1):1-10; doi:10.1112/blms/33.1.1
© 2001 by London Mathematical Society
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© London Mathematical Society

Eva Kallin's Lemma On Polynomial Convexity

P. J. De Paepe

Korteweg-de Vries Instituut, Universiteit van Amsterdam Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands; e-mail: depaepe{at}science.uva.nl

Received 17 May 1999. Revision received 4 November 1999. Revision received 19 January 2000.

We give a survey on the use of Eva Kallin's lemma. This lemma gives a condition on two polynomially convex sets in Cn under which their union is polynomially convex. This result has proved to be a useful tool in different areas of complex function theory of several variables, for instance in the study of polynomial convexity of the union of totally real surfaces, and in approximation problems in function algebras.


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