Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 7

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

An example of a subalgebra of $H^{∞}$ on the unit disk whose stable rank is not finite

100%
Mortini R.
Studia Mathematica
|
1992
|
tom 103
|
nr 3
275-281
EN
We present an example of a subalgebra with infinite stable rank in the algebra of all bounded analytic functions in the unit disk.
2
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

The Riemann-Cantor uniqueness theorem for unilateral trigonometric series via a special version of the Lusin-Privalov theorem

100%
Mortini R.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2017
|
tom 71
|
nr 1
EN
Using Baire's theorem, we give a very simple proof of a special version of the Lusin-Privalov theorem and deduce via Abel's  theorem the  Riemann-Cantor theorem on the uniqueness of the coefficients of pointwise convergent unilateral trigonometric series.
3
Content available remote

Embedding polydisk algebras into the disk algebra and an application to stable ranks

100%
Mortini R.
Annales Polonici Mathematici
|
2014
|
tom 112
|
nr 3
217-221
EN
It is shown how to embed the polydisk algebras (finite and infinite ones) into the disk algebra A(𝔻̅). As a consequence, one obtains uniform closed subalgebras of A(𝔻̅) which have arbitrarily prescribed stable ranks.
4
Content available remote

A constructive proof of the Beurling-Rudin theorem

100%
Mortini R.
Studia Mathematica
|
1998
|
tom 129
|
nr 1
51-58
EN
A constructive proof of the Beurling-Rudin theorem on the characterization of the closed ideals in the disk algebra A(𝔻) is given.
5
Content available remote

The Bourgain algebra of the disk algebra A(𝔻) and the algebra QA

64%
Cima J., Mortini R.
Studia Mathematica
|
1995
|
tom 113
|
nr 3
211-221
EN
It is shown that the Bourgain algebra $A(𝔻)_b$ of the disk algebra A(𝔻) with respect to $H^{∞}(𝔻)$ is the algebra generated by the Blaschke products having only a finite number of singularities. It is also proved that, with respect to $H^{∞}(𝔻)$, the algebra QA of bounded analytic functions of vanishing mean oscillation is invariant under the Bourgain map as is $A(𝔻)_b$.
6
Content available remote

Simultaneous stabilization in $A_{ℝ}(𝔻)$

64%
Mortini R., Wick B.
Studia Mathematica
|
2009
|
tom 191
|
nr 3
223-235
EN
We study the problem of simultaneous stabilization for the algebra $A_{ℝ}(𝔻)$. Invertible pairs $(f_{j},g_{j})$, j = 1,..., n, in a commutative unital algebra are called simultaneously stabilizable if there exists a pair (α,β) of elements such that $αf_{j} + βg_{j}$ is invertible in this algebra for j = 1,..., n. For n = 2, the simultaneous stabilization problem admits a positive solution for any data if and only if the Bass stable rank of the algebra is one. Since $A_{ℝ}(𝔻)$ has stable rank two, we are faced here with a different situation. When n = 2, necessary and sufficient conditions are given so that we have simultaneous stability in $A_{ℝ}(𝔻)$. For n ≥ 3 we show that under these conditions simultaneous stabilization is not possible and further connect this result to the question of which pairs (f,g) in $A_{ℝ}(𝔻)²$ are totally reducible, that is, for which pairs there exist two units u and v in $A_{ℝ}(𝔻)$ such that uf + vg = 1.
7
Content available remote

An upper bound for the distance to finitely generated ideals in Douglas algebras

51%
Gorkin P., Mortini R., Suárez D.
Studia Mathematica
|
2001
|
tom 148
|
nr 1
23-36
EN
Let f be a function in the Douglas algebra A and let I be a finitely generated ideal in A. We give an estimate for the distance from f to I that allows us to generalize a result obtained by Bourgain for $H^{∞}$ to arbitrary Douglas algebras.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.