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 $H^{\infty}$.

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 $|z|$.

scholarly journals WEIGHTED COMPOSITION OPERATORS ON H∞ ∩ o

2014 ◽  
Vol 57 (2) ◽  
pp. 475-480
Author(s):  
SHÛICHI OHNO
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Composition Operators ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Bounded Analytic Functions ◽  
Disk Algebra ◽  
Closed Subalgebra ◽  
Weighted Composition

AbstractWe will characterize the boundedness and compactness of weighted composition operators on the closed subalgebra H∞ ∩ $\mathcal{B}$o between the disk algebra and the space of bounded analytic functions on the open unit disk.

scholarly journals Partial sums of certain analytic functions

2001 ◽  
Vol 25 (12) ◽  
pp. 771-775 ◽  
Author(s):  
Shigeyoshi Owa
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Partial Sums ◽  
Open Unit ◽  
Open Unit Disk

The object of the present paper is to consider the starlikeness and convexity of partial sums of certain analytic functions in the open unit disk.

scholarly journals The order of convexity for an integral operator

2016 ◽  
Vol 32 (1) ◽  
pp. 123-129
Author(s):  
VIRGIL PESCAR ◽  
◽  
CONSTANTIN LUCIAN ALDEA ◽  
◽  
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Order Of Convexity

In this paper we consider an integral operator for analytic functions in the open unit disk and we derive the order of convexity for this integral operator, on certain classes of univalent functions.

scholarly journals Strong Differential Subordination Results for Multivalent Analytic Functions Associated with Dziok-Srivastava Operator

2019 ◽  
pp. 159-168
Author(s):  
Abbas Kareem Wanas ◽  
Hala Abbas Mehdi
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Closed Unit Disk ◽  
Strong Differential Subordination

In this paper, by making use of the principle of strong subordination, we establish some interesting properties of multivalent analytic functions defined in the open unit disk and closed unit disk of the complex plane associated with Dziok-Srivastava operator.

A Filter Description of the Homomorphisms of H∞

1965 ◽  
Vol 17 ◽  
pp. 734-757 ◽  
Author(s):  
A. Kerr-Lawson
Keyword(s):  
Unit Disk ◽  
Maximal Ideal ◽  
Continuous Mapping ◽  
Open Unit ◽  
Supremum Norm ◽  
Ideal Space ◽  
Open Unit Disk ◽  
Classical Theorem ◽  
Bounded Analytic Functions ◽  
The Hyperbolic Metric

The algebra of bounded analytic functions on the open unit disk D, usually written H∞ i is a commutative Banach algebra under the supremum norm. Since its compact maximal ideal space M (space of complex homomorphisms) is an extension space of the unit disk, there must be a continuous mapping form βD, the Stone-Čech compactification of D, onto M. R. C. Buck has remarked (4), that this mapping fails to be one-one, in the light of a classical theorem of Pick. If the points of βD are represented by filters of subsets of D, we can identify those filters which are sufficiently close in terms of the hyperbolic metric on D in an attempt to get a one-one correspondence between filters and points of M.

scholarly journals On Certain Classes of Convex Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Young Jae Sim ◽  
Oh Sang Kwon
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Real Numbers ◽  
Inverse Functions

For real numbersαandβsuch that0≤α<1<β, we denote by𝒦α,βthe class of normalized analytic functions which satisfy the following two sided-inequality:α<ℜ1+zf′′z/f′z<β  z∈𝕌,where𝕌denotes the open unit disk. We find some relationships involving functions in the class𝒦(α,β). And we estimate the bounds of coefficients and solve the Fekete-Szegö problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or biunivalent functions.

scholarly journals Kudriasov Type Univalence Criteria for Some Integral Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Virgil Pescar ◽  
Nicoleta Breaz
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Univalence Criteria

We consider some integral operators defined by analytic functions in the open unit disk and derive new univalence criteria for these operators, using Kudriasov condition for a function to be univalent.

scholarly journals Starlikeness of Functions Defined by Third-Order Differential Inequalities and Integral Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
R. Chandrashekar ◽  
Rosihan M. Ali ◽  
K. G. Subramanian ◽  
A. Swaminathan
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Inequalities ◽  
Third Order ◽  
Positive Order

Sufficient conditions are obtained to ensure starlikeness of positive order for analytic functions defined in the open unit disk satisfying certain third-order differential inequalities. As a consequence, conditions for starlikeness of functions defined by integral operators are obtained. Connections are also made to earlier known results.

Properties of the Salagean Operator

1998 ◽  
Vol 5 (4) ◽  
pp. 361-366
Author(s):  
Li Jian Lin ◽  
Shigeyoshi Owa
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Sălăgean Operator ◽  
Salagean Operator

Abstract The object of the present paper is to show the properties of the Salagean operator for analytic functions in the open unit disk. The main results obtained here extend and improve the earlier results obtained by several authors.

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