11 citations · 52 across the 22 of their papers we have counts for
14 papers · 1 filter
One-component inner functions II
Raymond Mortini, Joseph Cima
We continue our study of the set of inner functions in with the property that there is such that the level set $Ω_u(η):=\{z\in\mathbb D:…
One-component inner functions
Joseph Cima, Raymond Mortini
We explicitely unveil several classes of inner functions in with the property that there is such that the level set $Ω_u(η):=\{z\in\mathbb D: |u(z)|<η\}…
On the Krull Intersection Theorem in Function Algebras
Raymond Mortini, Rudolf Rupp, Amol Sasane
A version of the Krull Intersection Theorem states that for Noetherian domains, the Krull intersection of every proper ideal is trivial; that is $$ ki(I):=\displaystyle…
On a family of pseudohyperbolic disks
Raymond Mortini, Rudolf Rupp
Hyperbolic geometry plays an important role within function theory of the disk. For example, via the Schwarz-Pick Lemma, the isometries of the unit disk with respect to…
A short proof of Cartan's Nullstellensatz for entire functions in
Raymond Mortini
Using the fact that the maximal ideals in the polydisk algebra are given by the kernels of point evaluations, we derive a simple formula that gives a solution to the Bézout equatio…
Some curiosities of the algebra of bounded Dirichlet series
Raymond Mortini, Amol Sasane
It is shown that the algebra of bounded Dirichlet series is not a coherent ring, and has infinite Bass stable rank. As corollaries of the latter result, it is derived that the alge…
Holomorphic injective extensions of functions in P(K) and algebra generators
Raymond Mortini
We present necessary and sufficient conditions on planar compacta and continuous functions on in order that generates the algebras or . We…
Embedding polydisk algebras into the disk algebra and an application to stable ranks
Raymond Mortini
It is shown how to embed the polydisk algebras (finite and infinite ones) into the disk algebra . As a consequence, one obtains uniform closed subalgebras…
Noncoherence of some rings of holomorphic functions in several variables as an easy consequence of the one-variable case
Raymond Mortini, Amol Sasane
Using the facts that the disk algebra and the Wiener algebra are not coherent, we prove that the polydisc algebra, the ball algebra and the Wiener algebra of the polydisc are not c…
Corona-type theorems and division in some function algebras on planar domains
Raymond Mortini, Rudolf Rupp
Let be an algebra of bounded smooth functions on the interior of a compact set in the plane. We study the following problem: if satisfy $|f|\leq \sum_{j=…
Topological Stable Rank of for Circular Domains
Raymond Mortini, Rudolf Rupp, Amol Sasane +1
Let be a circular domain, that is, an open disk with finitely many closed disjoint disks removed. Denote by the Banach algebra of all bounded holomorphic function…
Spectral Characteristics and Stable Ranks for the Sarason Algebra
Raymond Mortini, Brett D. Wick
We prove a Corona type theorem with bounds for the Sarason algebra and determine its spectral characteristics. We also determine the Bass, the dense, and the topologic…
Simultaneous Stabilization in
Raymond Mortini, Brett D. Wick
In this note we study the problem of simultaneous stabilization for the algebra $A_\R(\D)$. Invertible pairs , , in a commutative unital algebra are called \…
The Corona theorem and stable rank for the algebra $\mC +BH^\infty$
Raymond Mortini, Amol Sasane, Brett D. Wick
Let be a Blaschke product. We prove in several different ways the corona theorem for the algebra $H^\infty_B:=\mC+BH^\infty$. That is, we show the equivalence of the classical…