<E, F> -Domains of Holomorphy

Abstract

This chapter, which is concerned with domains spread over the complex linear vector space E of a dual pair <E, F>, consists mainly of extensions of results for the special case (E due to M. Matos [M1, M2] (countable ⋀) and V. Aurich [A4] (arbitrary ⋀). (See also [H3, R6].) The dual pair <E, F> is fixed throughout and the topology in E is always assumed to be the σ(E, F)-topology. Also, instead of using the rather cumbersome expression, “[E, ℘ _{<E, F>} ]-domain”, for a domain spread over E, we shall use the simpler term, “<E, F>-domain”. Similarly, an <E, F>-domain of ℘ _{<E, F>} -holomorphy will be called simply an <E, F>-domain of holomorphy.