Pseudoconvex classes of functions. II. Affine pseudoconvex classes onRN
Zbigniew Słodkowski · Pacific Journal of Mathematics · 1990
A complete description of invariant pseudoconvex classes of functions on R N which are closed with respect to addition of affine functions is given.Each such class is shown to he equal to its own bidual, and approximation results, including piecewise-smooth approximation and a counterexample to smooth approximation, are obtained.The results of the paper have applications to multivariate interpolation of normed spaces and to approximation of analytic multifunctions, which are given elsewhere.