scholarly journals Some Characterizations of Weighted Holomorphic Function Classes by Univalent Function Classes

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
A. El-Sayed Ahmed ◽  
S. Omran
Keyword(s):  
Holomorphic Function ◽  
Univalent Function ◽  
Holomorphic Functions ◽  
Function Class ◽  
Function Classes ◽  
Type Classes ◽  
Schwarzian Derivatives ◽  
Type Spaces ◽  
High Utility ◽  
Formula Type

Some characterizations of Q K , ω p , q − type classes of holomorphic functions by Schwarzian derivatives with known conformal-type mappings are introduced in the present manuscript. Moreover, the action of the pre-Schwarzian derivatives on Q K , ω p , q − type classes, typically the univalent ones by using concerned Carleson-type measures, is investigated. In addition, we reveal important characterizations of some concerned weighted analytic-type spaces with the known Schwarzian derivatives evolving certain Q − type of concerned function class for a high utility toward practical and feasible application of concerned domains.

scholarly journals Traces of certain classes of holomorphic functions on finite unions of Carleson sequences

1999 ◽  
Vol 41 (1) ◽  
pp. 103-114 ◽  
Author(s):  
ANDREAS HARTMANN
Keyword(s):  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions ◽  
Hardy Classes ◽  
Type Spaces ◽  
Trace Spaces

We give a method allowing the generalization of the description of trace spaces of certain classes of holomorphic functions on Carleson sequences to finite unions of Carleson sequences. We apply the result to different classes of spaces of holomorphic functions such as Hardy classes and Bergman type spaces.

scholarly journals On Some Subclasses of $m$-fold Symmetric Bi-univalent Functions associated with the Sakaguchi Type Functions

2021 ◽  
pp. 1-15
Author(s):  
Ismaila O. Ibrahim ◽  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk

In the present investigation, we introduce the subclasses $\Lambda_{\Sigma_m}^{\rightthreetimes}(\sigma,\phi,\upsilon)$ and $\Lambda_{\Sigma_m}^{\rightthreetimes}(\sigma,\gamma,\upsilon)$ of $m$-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the Sakaguchi type of functions and defined in the open unit disk. Further, we obtain estimates on the initial coefficients $b_{m+1}$ and $b_{2m+1}$ for the functions of these subclasses and find out connections with some of the familiar classes.

Coefficient Estimates for Certain Subclasses of m-Fold Symmetric Bi-univalent Functions Associated with Pseudo-Starlike Functions

2021 ◽  
pp. 209-223
Author(s):  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In the present investigation, we introduce the subclasses $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\phi)$ and $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\delta)$ of \textit{m}-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the pseudo-starlike functions and defined in the open unit disk $\mathbb{U}$. Moreover, we obtain estimates on the initial coefficients $|b_{m+1}|$ and $|b_{2m+1}|$ for the functions belong to these subclasses and identified correlations with some of the earlier known classes.

scholarly journals Isometric and Closed-Range Composition Operators between Bloch-Type Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-15
Author(s):  
Nina Zorboska
Keyword(s):  
Holomorphic Function ◽  
Composition Operators ◽  
Function Spaces ◽  
Complete Characterization ◽  
Closed Range ◽  
Different Types ◽  
Type Spaces ◽  
Range Determination

We present an overview of the known results describing the isometric and closed-range composition operators on different types of holomorphic function spaces. We add new results and give a complete characterization of the isometric univalently induced composition operators acting between Bloch-type spaces. We also add few results on the closed-range determination of composition operators on Bloch-type spaces and present the problems that are still open.

scholarly journals Boundary behaviour of holomorphic functions on the cardioid domain with some applications

2019 ◽  
Vol 38 (7) ◽  
pp. 203-218
Author(s):  
Shatha Sami Alhily ◽  
_ Deepmala
Keyword(s):  
General Solution ◽  
Holomorphic Function ◽  
Unit Disk ◽  
Laplace Equation ◽  
Holomorphic Functions ◽  
Research Paper ◽  
Boundary Behaviour ◽  
Polar Function

The objective of this research paper is to show how the Bennan'sconjecture  become a useful tool  to construct a holomorphic function on the cardioid domain, and on the boundary of unit disk. Moreover , we have addressed some applications on the existence of cusp on the boundary of arising from integrability of conformalmaps through one of the polar function in the general solution of Laplace equation.

scholarly journals ON THE ANNIHILATOR OF A DOLBEAULT GROUP

2010 ◽  
Vol 21 (03) ◽  
pp. 317-331
Author(s):  
IMRE PATYI
Keyword(s):  
Holomorphic Function ◽  
Open Subset ◽  
Cohomology Group ◽  
Holomorphic Functions ◽  
Dolbeault Cohomology ◽  
Infinite Dimensional ◽  
Continuous Character

We show that any Dolbeault cohomology group Hp,q(D), p ≥ 0, q ≥ 1, of an open subset D of a closed finite codimensional complex Hilbert submanifold of ℓ2 is either zero or infinite dimensional. We also show that any continuous character of the algebra of holomorphic functions of a closed complex Hilbert submanifold M of ℓ2 is induced by its evaluation at a point of M. Lastly, we prove that any closed split infinite dimensional complex Banach submanifold of ℓ2 admits a nowhere critical holomorphic function.

A POLAR DECOMPOSITION FOR HOLOMORPHIC FUNCTIONS ON A STRIP

2001 ◽  
Vol 33 (3) ◽  
pp. 309-319 ◽  
Author(s):  
KONRAD SCHMÜDGEN
Keyword(s):  
Holomorphic Function ◽  
Real Axis ◽  
Polar Decomposition ◽  
Holomorphic Functions ◽  
Heisenberg Algebra ◽  
Boundary Values ◽  
Operator Representation ◽  
The Real ◽  
Almost Everywhere

Let f be a holomorphic function on the strip {z ∈ [Copf ] : −α < Im z < α}, where α > 0, belonging to the class [Hscr ](α,−α;ε) defined below. It is shown that there exist holomorphic functions w1 on {z ∈ [Copf ] : 0 < Im z < 2α} and w2 on {z ∈ [Copf ] : −2α < Im z < 2α}, such that w1 and w2 have boundary values of modulus one on the real axis, and satisfy the relationsw1(z)=f(z-αi)w2(z-2αi) and w2(z+2αi)=f(z+αi)w1(z)for 0 < Im z < 2α, where f(z) := f(z). This leads to a ‘polar decomposition’ f(z) = uf(z + αi)gf(z) of the function f(z), where uf (z + αi) and gf(z) are holomorphic functions for −α < Im z < α, such that [mid ]uf(x)[mid ] = 1 and gf(x) [ges ] 0 almost everywhere on the real axis. As a byproduct, an operator representation of a q-deformed Heisenberg algebra is developed.

AN EXTENDED STOCHASTIC INTEGRAL AND A WICK CALCULUS ON PARAMETRIZED KONDRATIEV-TYPE SPACES OF MEIXNER WHITE NOISE

2008 ◽  
Vol 11 (04) ◽  
pp. 541-564 ◽  
Author(s):  
N. A. KACHANOVSKY
Keyword(s):  
White Noise ◽  
Stochastic Equation ◽  
Stochastic Integral ◽  
Holomorphic Functions ◽  
Generalized Functions ◽  
Wick Product ◽  
Stochastic Integration ◽  
Type Spaces ◽  
Wick Calculus

Using a general approach that covers the cases of Gaussian, Poissonian, Gamma, Pascal and Meixner measures, we consider an extended stochastic integral and construct elements of a Wick calculus on parametrized Kondratiev-type spaces of generalized functions; consider the interconnection between the extended stochastic integration and the Wick calculus; and give an example of a stochastic equation with a Wick-type nonlinearity. The main results consist of studying the properties of the extended (Skorohod) stichastic integral subject to the particular spaces under consideration; and of studying the properties of a Wick product and Wick versions of holomorphic functions on the parametrized Kondratiev-type spaces. These results are necessary, in particular, in order to describe properties of solutions of normally ordered white noise equations in the "Meixner analysis".

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