scholarly journals Approximation by invertible functions of $H^{\infty}$

2006 ◽  
Vol 99 (2) ◽  
pp. 287 ◽  
Author(s):  
Artur Nicolau ◽  
Daniel Suárez
Keyword(s):  
Banach Algebra ◽  
Unit Disk ◽  
Analytic Functions ◽  
Banach Algebras ◽  
Bounded Analytic Functions ◽  
Analytic Proof ◽  
Dense Image

We provide an analytic proof that if $H^\infty$ is the algebra of bounded analytic functions on the unit disk, $A$ is a Banach algebra and $f: H^\infty \rightarrow A$ is a Banach algebras morphism with dense image, then $f((H^\infty)^{-1})$ is dense in $A^{-1}$.

LIPSCHITZ-TYPE INEQUALITIES FOR ANALYTIC FUNCTIONS IN BANACH ALGEBRAS

2019 ◽  
Vol 100 (3) ◽  
pp. 489-497
Author(s):  
SILVESTRU SEVER DRAGOMIR
Keyword(s):  
Analytic Function ◽  
Banach Algebra ◽  
Analytic Functions ◽  
Banach Algebras ◽  
Logarithmic Functions

In this paper we provide some bounds for the quantity $\Vert f(y)-f(x)\Vert$, where $f:D\rightarrow \mathbb{C}$ is an analytic function on the domain $D\subset \mathbb{C}$ and $x$, $y\in {\mathcal{B}}$, a Banach algebra, with the spectra $\unicode[STIX]{x1D70E}(x)$, $\unicode[STIX]{x1D70E}(y)\subset D$. Applications for the exponential and logarithmic functions on the Banach algebra ${\mathcal{B}}$ are also given.

ESTIMATES OF THE SECOND DERIVATIVE OF BOUNDED ANALYTIC FUNCTIONS

2019 ◽  
Vol 100 (3) ◽  
pp. 458-469
Author(s):  
GANGQIANG CHEN
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Upper Bound ◽  
Analytic Functions ◽  
Open Unit ◽  
Second Derivative ◽  
Open Unit Disk ◽  
Bounded Analytic Functions ◽  
Schwarz’S Lemma

Assume a point $z$ lies in the open unit disk $\mathbb{D}$ of the complex plane $\mathbb{C}$ and $f$ is an analytic self-map of $\mathbb{D}$ fixing 0. Then Schwarz’s lemma gives $|f(z)|\leq |z|$, and Dieudonné’s lemma asserts that $|f^{\prime }(z)|\leq \min \{1,(1+|z|^{2})/(4|z|(1-|z|^{2}))\}$. We prove a sharp upper bound for $|f^{\prime \prime }(z)|$ depending only on $|z|$.

Analysis on Sparse Parts in the Maximal Ideal Space of H∞

1992 ◽  
Vol 44 (4) ◽  
pp. 805-823
Author(s):  
Keiji izuchi
Keyword(s):  
Banach Algebra ◽  
Maximal Ideal ◽  
Analytic Functions ◽  
Level Sets ◽  
Maximal Ideal Space ◽  
Ideal Space ◽  
Bounded Analytic Functions ◽  
Douglas Algebras

AbstractAnalysis on sparse parts of the Banach algebra of bounded analytic functions is given. It is proved that Sarason's theorem for QC-level sets cannot be generalized to general Douglas algebras.

scholarly journals Global Holomorphic Functions in Several Non-Commuting Variables II

2018 ◽  
Vol 61 (3) ◽  
pp. 458-463 ◽  
Author(s):  
Jim Agler ◽  
John McCarthy
Keyword(s):  
Transfer Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Holomorphic Functions ◽  
Bounded Analytic Functions

AbstractWe give a new proof that bounded non-commutative functions on polynomial polyhedra can be represented by a realization formula, a generalization of the transfer function realization formula for bounded analytic functions on the unit disk.

scholarly journals Convolution properties of a class of bounded analytic functions

1992 ◽  
Vol 45 (1) ◽  
pp. 9-23 ◽  
Author(s):  
Zou Zhongzhu ◽  
Shigeyoshi Owa
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Bounded Analytic Functions ◽  
Class A ◽  
Convolution Properties ◽  
Class Of Functions

Let A be the class of functions f(z) which are analytic in the unit disk U with f(0) = f′(0) - 1 = 0. A subclass S(λ, M) (λ > 0, M > 0) of A is introduced. The object of the present paper is to prove some interesting convolution properties of functions f(z) belonging to the class S(λ, M). Also a certain integral operator J for f(z) in the class A is considered.

scholarly journals Validity of Closed Ideals in Algebras of Series of Square Analytic Functions

2021 ◽  
Vol 5 (1) ◽  
pp. p20
Author(s):  
Musa Siddig ◽  
Shawgy Hussein ◽  
Amani Elseid
Keyword(s):  
Banach Algebra ◽  
Unit Disk ◽  
Analytic Functions ◽  
Dirichlet Space ◽  
Commutative Banach Algebra ◽  
Square Functions

We show the validity of a complete description of closed ideals of the algebra which is a commutative Banach algebra , that endowed with a pointwise operations act on Dirichlet space of algebra of series of analytic functions on the unit disk  satisfying the Lipscitz condition of order of square sequence  obtained by (Brahim Bouya, 2008), we introduce and deal with approximation square functions which is an outer functions to produce and show results in .

scholarly journals Factorization for bounded analytic functions in the unit disk and an application to prime ideals

2006 ◽  
Vol 99 (2) ◽  
pp. 168 ◽  
Author(s):  
Raymond Mortini
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Prime Ideals ◽  
Open Unit ◽  
Open Unit Disk ◽  
Finitely Generated ◽  
Bounded Analytic Functions

We prove several factorization theorems for bounded analytic functions in the open unit disk and present a very simple new proof of two conjectures of Frank Forelli and the author on the structure of finitely generated, respectively countably generated prime ideals in $H^{\infty}$.

scholarly journals Multipliers

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1277-1283 ◽  
Author(s):  
Miroljub Jevtic
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Mixed Norm ◽  
Bounded Analytic Functions ◽  
Mixed Norm Spaces ◽  
Spaces Of Analytic Functions

We describe the multiplier spaces (Hp,q,?,H?), and (Hp,q,?,H?,v,?), where Hp,q,? are mixed norm spaces of analytic functions in the unit disk D and H? is the space of bounded analytic functions in D. We extend some results from [7] and [3], particularly Theorem 4.3 in [3].

scholarly journals Ideals generated by singular inner functions

1980 ◽  
Vol 21 (2) ◽  
pp. 237-252
Author(s):  
Michael von Renteln
Keyword(s):  
Banach Algebra ◽  
Analytic Functions ◽  
Unit Disc ◽  
Boundary Behavior ◽  
Independent Interest ◽  
Inner Function ◽  
Inner Functions ◽  
Bounded Analytic Functions ◽  
Local Boundary ◽  
The Ideal

Singular inner functions are in many respects the most important and difficult type of functions in the Banach algebra H∞ of bounded analytic functions in the unit disc. This paper is concerned with ideals generated by singular inner functions. In particular, conditions on the associated measures are given so that the ideal spans the whole algebra H∞. To this end the local boundary behavior of a singular inner function is studied and the results obtained there may be of independent interest.

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