Vol. 92, No. 1, 1981

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Approximation by rational modules on boundary sets

James Li-Ming Wang

Vol. 92 (1981), No. 1, 237–239
Abstract

Let X be a compact subset of the complex plane. Let the module (X)𝒫m be the space of all functions of the form

r0(z)+ r1(z)z + ⋅⋅⋅+ rm (z)zm

where each ri is a rational function with poles off X. We prove that (X)𝒫1 is dense in Lp(∂X) for all 1 p < .

Mathematical Subject Classification 2000
Primary: 30E10
Milestones
Received: 13 February 1979
Revised: 15 February 1980
Published: 1 January 1981
Authors
James Li-Ming Wang