scholarly journals Geometric Properties for a family of p-valent Holomorphic Functions with Negative Coefficients for Operator on Hilbert Space

2018 ◽  
Vol 10 (2) ◽  
Keyword(s):  
Hilbert Space ◽  
Holomorphic Functions ◽  
Geometric Properties

Geometric properties for a family of holomorphic functions associated with Wanas operator defined on complex Hilbert space

2020 ◽  
pp. 2150122
Author(s):  
Abbas Karem Wanas ◽  
Junesang Choi ◽  
Nak Eun Cho
Keyword(s):  
Hilbert Space ◽  
Extreme Points ◽  
Holomorphic Functions ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties

By making use of Wanas operator, we aim to introduce and investigate a certain family of univalent holomorphic functions with negative coefficients defined on complex Hilbert space. We present some important geometric properties of this family such as coefficient estimates, convexity, distortion and growth, radii of starlikeness and convexity. We also discuss the extreme points for functions belonging to this family.

Extension of polynomials defined on subspaces

2010 ◽  
Vol 148 (3) ◽  
pp. 505-518 ◽  
Author(s):  
MAITE FERNÁNDEZ-UNZUETA ◽  
ÁNGELES PRIETO
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Homogeneous Polynomial ◽  
Analogous Result ◽  
Holomorphic Functions ◽  
Bounded Norm ◽  
Uniformly Bounded

AbstractLet k ∈ ℕ and let E be a Banach space such that every k-homogeneous polynomial defined on a subspace of E has an extension to E. We prove that every norm one k-homogeneous polynomial, defined on a subspace, has an extension with a uniformly bounded norm. The analogous result for holomorphic functions of bounded type is obtained. We also prove that given an arbitrary subspace F ⊂ E, there exists a continuous morphism φk, F: (kF) → (kE) satisfying φk, F(P)|F = P, if and only E is isomorphic to a Hilbert space.

scholarly journals A HOLOMORPHIC REPRESENTATION OF THE JACOBI ALGEBRA

2006 ◽  
Vol 18 (02) ◽  
pp. 163-199 ◽  
Author(s):  
STEFAN BERCEANU
Keyword(s):  
Hilbert Space ◽  
Differential Operators ◽  
Holomorphic Functions ◽  
First Order ◽  
Polynomial Coefficients ◽  
Holomorphic Representation

A representation of the Jacobi algebra 𝔥1 ⋊ 𝔰𝔲(1, 1) by first-order differential operators with polynomial coefficients on the manifold [Formula: see text] is presented. The Hilbert space of holomorphic functions on which the holomorphic first-order differential operators with polynomials coefficients act is constructed.

scholarly journals A Certain Subclass of Multivalent Analytic Functions with Negative Coefficients for Operator on Hilbert Space

2019 ◽  
pp. 355-364
Author(s):  
Asraa Abdul Jaleel Husien
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Convex Set ◽  
Extreme Points ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties

In the present work, we introduce and study a certain subclass for multivalent analytic functions with negative coefficients defined on complex Hilbert space. We establish a number of geometric properties, like, coefficient estimates, convex set, extreme points and radii of starlikeness and convexity.

scholarly journals New Family of Multivalent Analytic Functions Defined on Complex Hilbert Space

2020 ◽  
pp. 155-165 ◽  
Author(s):  
Abbas Kareem Wanas ◽  
S. R. Swamy
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Convex Set ◽  
Extreme Points ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class ◽  
New Family

In this article, we define a certain new class of multivalent analytic functions with negative coefficients on complex Hilbert space. We derive a number of important geometric properties, such as, coefficient estimates, radii of starlikeness and convexity, extreme points and convex set.

Geometric Characterizations of Hilbert Spaces

2016 ◽  
Vol 59 (4) ◽  
pp. 769-775
Author(s):  
Francisco Javier García-Pacheco ◽  
Justin R. Hill
Keyword(s):  
Hilbert Space ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Geometric Properties ◽  
Generic Element

AbstractWe study some geometric properties related to the setobtaining two characterizations of Hilbert spaces in the category of Banach spaces. We also compute the distance of a generic element (h, k) ∊ for H a Hilbert space.

scholarly journals TAYLOR MAP ON GROUPS ASSOCIATED WITH A II1-FACTOR

2002 ◽  
Vol 05 (01) ◽  
pp. 93-111 ◽  
Author(s):  
MARIA GORDINA
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Stochastic Differential Equation ◽  
Heat Kernel ◽  
Holomorphic Functions ◽  
Taylor Map ◽  
Invertible Elements

A notion of the heat kernel measure is introduced for the L2 completion of a hyperfinite II1-factor with respect to the trace. Some properties of this measure are derived from the corresponding stochastic differential equation. Then the Taylor map is studied for a space of holomorphic functions square integrable with respect to the heat kernel measure. We also define a skeleton map from this space to a Hilbert space of holomorphic functions on a certain Cameron–Martin group. This group is a subgroup of the group of invertible elements of the II1-factor.

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