Invariant subspaces on open Riemann surfaces

Morisuke Hasumi

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Invariant subspaces on open Riemann surfaces. II

Morisuke Hasumi (1976)

Annales de l'institut Fourier

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We considerably improve our earlier results [Ann. Inst. Fourier, 24-4 (1974] concerning Cauchy-Read’s theorems, convergence of Green lines, and the structure of invariant subspaces for a class of hyperbolic Riemann surfaces.

Analytic functions in a lacunary end of a Riemann surface

Zenjiro Kuramochi (1975)

Annales de l'institut Fourier

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Let $G$ be an end of a Riemann surface with null boundary and let $G^{'}$ be a lacunary end with a closed set $F = G - G^{'}$ . We study minimal functions in $G$ and $G^{'}$ to show that $G$ and $G^{'}$ have similar properties if $F$ is thinly distributed on the ideal boundary. We discuss the behaviour of analytic functions in $G^{'}$ and relation between the existence of analytic functions of some classes in $G^{'}$ and the structure of Martin’s boundary points over the end $G$ . Also we show that the existence of complicated Martin’s boundary...

On $Φ$ -bounded harmonic functions

Mitsuru Nakai (1966)

Annales de l'institut Fourier

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Soit $Φ$ une fonction non négative réelle ; une fonction $u$ harmonique sur une surface de Riemann $R$ est dite $Φ$ -bornée si $Φ (| u |)$ admet une majorante harmonique. On étudie la classe $H Φ (R)$ des fonctions $Φ$ -bornées sur $R$ et on montre, en particulier, que chaque $u$ de $H Φ (R)$ est essentiellement positive pour toute $R$ , si et seulement si $\inf_{t \to \infty} Φ (t) / t > 0$ .

Composition operators: $N_{α}$ to the Bloch space to $Q_{β}$

Jie Xiao (2000)

Studia Mathematica

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Let $N_{α}$ ,B and Qβ be the weighted Nevanlinna space, the Bloch space and the Q space, respectively. Note that B and $Q_{β}$ are Möbius invariant, but $N_{α}$ is not. We characterize, in function-theoretic terms, when the composition operator $C_{ϕ} f = f ◦ ϕ$ induced by an analytic self-map ϕ of the unit disk defines an operator $C_{ϕ} : N_{α} \to B$ , $B \to Q_{β}$ , $N_{α} \to Q_{β}$ which is bounded resp. compact.

A maximal regular boundary for solutions of elliptic differential equations

Peter Loeb, Bertram Walsh (1968)

Annales de l'institut Fourier

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Soit $𝒜$ une classe harmonique de Brelot, définie sur $W$ . Il est donné un critère de régularité en termes de barrières, pour les points d’une frontière idéale. Soit $ℌ$ un sous-treillis banachique de ${ℬ𝒜}_{W}$ . Si $𝒜$ est hyperbolique, la frontière idéale compactifiante déterminée par $ℌ$ contient une “frontière harmonique” $Γ_{ℌ}$ qui satisfait le critère de régularité et $ℌ ≅ 𝒞_{R} (Γ_{ℌ})$ . Entre autres applications, on a la théorie des frontières de Wiener et Royden et des comparaisons de classes harmoniques.

Moebius-invariant algebras in balls

Walter Rudin (1983)

Annales de l'institut Fourier

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It is proved that the Fréchet algebra $C (B)$ has exactly three closed subalgebras $Y$ which contain nonconstant functions and which are invariant, in the sense that $f \circ Ψ \in Y$ whenever $f \in Y$ and $Ψ$ is a biholomorphic map of the open unit ball $B$ of $C^{n}$ onto $B$ . One of these consists of the holomorphic functions in $B$ , the second consists of those whose complex conjugates are holomorphic, and the third is $C (B)$ .

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