The Nevanlinna algebras, $_{α}^{p}$ , of this paper are the $L^{p}$ variants of classical weighted area Nevanlinna classes of analytic functions on = z ∈ ℂ: |z| < 1. They are F-algebras, neither locally bounded nor locally convex, with a rich duality structure. For s = (α+2)/p, the algebra $F_{s}$ of analytic functions f: → ℂ such that ${(1 - | z |)}^{s} | f (z) | \to 0$ as |z| → 1 is the Fréchet envelope of $_{α}^{p}$ . The corresponding algebra $_{s}^{\infty}$ of analytic f: → ℂ such that $s u p_{z \in} {(1 - | z |)}^{s} | f (z) | < \infty$ is a complete metric space but fails to be a topological vector space. $F_{s}$ is also...

Page 1

Download Results (CSV)

Advanced Search

Formula preview

Currently displaying 1 – 5 of 5

Dualität und Marinescu-Räume.

Striktheit von (LF)-Räumen.

On Tensor Algebras of Marinescu Spaces.

Zur Theorie der quasitonnelierten Räume.

Nevanlinna algebras