Invariant subspaces on open Riemann surfaces. II

Morisuke Hasumi

Displaying similar documents to “Invariant subspaces on open Riemann surfaces. II”

Invariant subspaces on open Riemann surfaces

Morisuke Hasumi (1974)

Annales de l'institut Fourier

Similarity:

Let $R$ be a hyperbolic Riemann surface, $d_{χ}$ a harmonic measure supported on the Martin boundary of $R$ , and $H^{\infty} (d χ)$ the subalgebra of $L^{\infty} (d χ)$ consisting of the boundary values of bounded analytic functions on $R$ . This paper gives a complete classification of the closed $H^{\infty} (d χ)$ -submodules of $L^{p} (d χ)$ , $1 \leq p \leq \infty$ (weakly $^{*}$ closed, if $p = \infty$ , when $R$ is regular and admits a sufficiently large family of bounded multiplicative analytic functions satisfying an approximation condition. It also gives, as a corollary, a corresponding result...

Some remarks on the Nevanlinna theory of holomorphic mappings of Riemann surfaces

Alois Klíč (1980)

Časopis pro pěstování matematiky

Similarity:

The higher topological form of Plateau's problem

Jesse Douglas (1939)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

On exceptional values of holomorphic mappings of Riemann surfaces

Alois Klíč (1980)

Časopis pro pěstování matematiky

Similarity:

Two remarks on Riemann surfaces.

José M. Rodriguez (1994)

Publicacions Matemàtiques

Similarity:

We study the relationship between linear isoperimetric inequalities and the existence of non-constant positive harmonic functions on Riemann surfaces. We also study the relationship between growth conditions of length of spheres and the existence and the existence of Green's function on Riemann surfaces.

Koebe's general uniformisation theorem for planar Riemann surfaces

Gollakota V. V. Hemasundar (2011)

Annales Polonici Mathematici

Similarity:

We give a complete and transparent proof of Koebe's General Uniformisation Theorem that every planar Riemann surface is biholomorphic to a domain in the Riemann sphere ℂ̂, by showing that a domain with analytic boundary and at least two boundary components on a planar Riemann surface is biholomorphic to a circular-slit annulus in ℂ.

An indestructible Blaschke product in the little Bloch space.

Christopher J. Bishop (1993)

Publicacions Matemàtiques

Similarity:

The little Bloch space, B, is the space of all holomorphic functions f on the unit disk such that lim lf'(z)l (1- lzl) = 0. Finite Blaschke products are clearly in B, but examples of infinite products in B are more difficult to obtain (there are now several constructions due to Sarason, Stephenson and the author, among others). Stephenson has asked whether B contains an infinite, indestructible Blaschke product, i.e., a Blaschke product B so that (B(z) - a)/(1 - âB(z)), is also a Blaschke...