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The Product of Automorphic Weighted Composition Operators on Hardy Space H <sup>2</sup>
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Abstract<p>Let <inline-formula> <tex-math><?CDATA $n\in {\mathbb{N}},{p}_{i}\in {\rm{U}},{\alpha }_{{P}_{i}}(z)=\frac{{p}_{i}-z}{1-{\bar{p}}_{i}z}(z\in {\rm{U}})$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <mi>n</mi> <mo>∈</mo> <mi>ℕ</mi> <mo>,</mo> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>∈</mo> <mi mathvariant="normal">U</mi> <mo>,</mo> <msub> <mi>α</mi> <mrow> <msub> <mi>P</mi> <mi>i</mi> </msub> </mrow> </msub> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mfrac> <mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>−</mo> <mi>z</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <msub> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> <mi>i</mi> </msub> <mi>z</mi> </mrow> </mfrac> <mo stretchy="false">(</mo> <mi>z</mi> <mo>∈</mo> <mi mathvariant="normal">U</mi> <mo stretchy="false">)</mo> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012045_ieqn1.gif" xlink:type="simple"></inline-graphic> </inline-formula>, and let <inline-formula> <tex-math><?CDATA ${f}_{1}\in {H}^{\infty },i=1,\ldots,n$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>∈</mo> <msup> <mi>H</mi> <mi>∞</mi> </msup> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012045_ieqn2.gif" xlink:type="simple"></inline-graphic> </inline-formula>. We discuss the relation between the points <italic>p<sub>i</sub> </italic> in U and the functions <italic>f<sub>i</sub> </italic> in U and the properties of the product of automorphic weighted composition operators <inline-formula> <tex-math><?CDATA ${W}_{{f}_{1},{\alpha }_{{p}_{1}}}\,{W}_{{f}_{2},{\alpha }_{{p}_{2}}}\ldots {W}_{{f}_{i},{\alpha }_{pi}}$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <msub> <mi>W</mi> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>α</mi> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> </mrow> </msub> </mrow> </msub> <mspace width="0.25em"></mspace> <msub> <mi>W</mi> <mrow> <msub> <mi>f</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>α</mi> <mrow> <msub> <mi>p</mi> <mn>2</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>…</mo> <msub> <mi>W</mi> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>α</mi> <mrow> <mi>p</mi> <mi>i</mi> </mrow> </msub> </mrow> </msub> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012045_ieqn3.gif" xlink:type="simple"></inline-graphic> </inline-formula> on Hardy space H<sup>2</sup>. In fact, it is very nice connection between analytic function theory and operator theory. In this paper, we give the sufficient and necessary conditions to be normal, unitary, hermitian operator on <italic>H</italic> <sup>2</sup> and we shall present the shape of the numerical range of it.</p>
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Publication Date
Sat Dec 01 2012
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Journal Of Economics And Administrative Sciences
Relationship of environmental costs to product life cycle costs Applied in the General Company for Battery Industry
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The relationship between costs of environment and costs of product life – cycle.    Boubtlessly when the economical unit exercise their productive works, they lead to pollution in water, air and soil as well as all stages of product life- cycle from Rans Dstage, production stage, packaging stage and finally abandonment stage-             Pollution causes environmental costs. Lgnoring or hiding environmental costs and no taking them in consideration with product cost lead to a wrong account of preduot cost.

Therefore, environmental costs should be included and matched for all stages with in product costs to know which activities, processes

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Thu May 14 2020
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The Impact of the Method of Dealing with the Product of Wars in the Continuity of the Crisis Wars. Beirut city as an Example
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This research investigates the subject of the impact of wars (as a manifestation of crisis) on architecture, and the extent of continuing wars physical and moral results of wars, even after the end of the cause of the crisis. The impact of different rebuilding which exposed to the effects of the war seems different in crisis regions.

The problem of research is about the uncertainty of the impact of the way chooses for reconstructing the buildings after wars in the continuity of the crisis of war. The goals of this research are to clarify the influence of methods of reconstruction of buildings in a city chosen which is Beirut, on the continuation of the war crisis with the argument of demolishing and rebuilding newly or keeping tr

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Wed Jan 01 2025
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Detection of the most frequent sources of dust storms in Iraq during 2020–2023 using space tools
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Dust storms are typical in arid and semi-arid regions such as the Middle East; the frequency and severity of dust storms have grown dramatically in Iraq in recent years. This paper identifies the dust storm sources in Iraq using remotely sensed data from Meteosat-spinning enhanced visible and infrared imager (SEVIRI) bands. Extracted combined satellite images and simulated frontal dust storm trajectories, using the Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) model, are used to identify the most influential sources in the Middle East and Iraq. Out of 132 dust storms in Iraq during 2020–2023, the most frequent occurred in the spring and summer. A dust source frequency percentage map (DSFPM) is generated using ArcGIS so

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Synthesis and characterization of ( L- proline ) amino acid with (Mn+2 , Fe+2 , Co+2 , Zn+2 and Cd+2 )
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Comparison of weighted estimated method and proposed method (BEMW) for estimation of semi-parametric model under incomplete data
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Generally, statistical methods are used in various fields of science, especially in the research field, in which Statistical analysis is carried out by adopting several techniques, according to the nature of the study and its objectives. One of these techniques is building statistical models, which is done through regression models. This technique is considered one of the most important statistical methods for studying the relationship between a dependent variable, also called (the response variable) and the other variables, called covariate variables. This research describes the estimation of the partial linear regression model, as well as the estimation of the “missing at random” values (MAR). Regarding the

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Wed May 17 2023
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Development of Quality Rating Evaluation of Outgoing Product Case Study Applied at the General Company for Vegetable Oils
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Research covers the uses the method of Quality Rating Evaluation to evaluate the
quality of production through which a determination of product quality of its production in
order to determine the amount of sales hence the profits for the company. The most important
function is to satisfy consumer at reasonable prices. Methods were applied to the product
(toothpaste) in the General Company for Vegetable Oil – Almaamoon Factory .
The company's has obtained ISO-certified (ISO 9001-2008). Random samples of
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Product development For Use Some Of The Lean Production Tools A Practical Research in the General Company for the automotive industry
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Mon Dec 31 2018
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Iraqi EFL Students’ Difficulties in Writing Composition: An Experimental Study (University of Baghdad)
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Iraqi EFL students face difficulties in writing composition, especially academic writing, which affects negatively their exam results. This study has been conducted in the Department of English at College of Education for Women, University of Baghdad, in order to identify first year EFL students&rsquo; incompetence in writing. This may enhance their achievement by some weekly writing activities. It deals with Iraqi EFL students&rsquo; difficulties in writing paragraphs such as descriptive, process, opinion, and factual paragraphs. The study aims to identify these difficulties and to suggest suitable solutions for them. The researcher perceives that it is necessary to enhance students&rsquo; skills in writing because it i

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Tue Dec 15 2020
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Acculturation and its Evolutionary Tendency in the Design of the Prayer Space Elements / Niche – A model: آلاء طالب كريم
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The peculiarity of worship spaces in the Islamic architecture is evident by its symbolic connotations with doctrinal connections, thus the niche has a major status in that symbolic connotation, which transformed due to the cultural interaction from a rock on the wall directed towards Mecca into an element of integrated structural entity with performative and aesthetic characteristics. The spread of the Islamic religion contributed to subjecting it to a design acculturation process, thus the problem of the research was raised by the following question: has the evolutionary tendency of acculturation been able to effect a major transformation in the niche design? The research aims at identifying the design acculturation and its translation

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Crossref
Publication Date
Fri Jan 01 2016
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A New Abnormality Detection Approach for T1-Weighted Magnetic Resonance Imaging Brain Slices Using Three Planes
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Generally, radiologists analyse the Magnetic Resonance Imaging (MRI) by visual inspection to detect and identify the presence of tumour or abnormal tissue in brain MR images. The huge number of such MR images makes this visual interpretation process, not only laborious and expensive but often erroneous. Furthermore, the human eye and brain sensitivity to elucidate such images gets reduced with the increase of number of cases, especially when only some slices contain information of the affected area. Therefore, an automated system for the analysis and classification of MR images is mandatory. In this paper, we propose a new method for abnormality detection from T1-Weighted MRI of human head scans using three planes, including axial plane, co

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