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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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Sat Oct 01 2022
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Preparation and study effect of vacuum annealing on structure and optical properties of AgCuInSe<inf>2</inf> thin film
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Thu Dec 01 2016
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Synthesis and Characterization of Some Anti-bacterial Active Transition Metal Complexes of N'-[2-(2-Phenyl hydrazinyl) Phenyl] Benzothiohydrazide
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THE RELATIVE CONSTANT TO ESTIMATE ̅ 2 OF 3–WAY AND DOUBLE CROSSES OF MAIZE
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A field experiment was conducted at the field of the Dept. of Field Crop Sci. / College of Agriculture / University of Baghdad . The objective was to determine the values of relative constant of three – way and double crosses of maize . Ten inbreds were used and crossed during spring and fall seasons of 2009 to produce three - way and double crosses , and ten hybrids were taken from each group . The ten hybrids were grown and selfed during spring 2010 to produce 2 seed . Three way and double crosses were sown with their parents and 2 seed during fall 2010 in RCBD with four replicates . Leaf area , total dry matter , row/ear , grain/ear , grain weight and grain weight/plant of hybrids , parents and 2 plants were taken . Results showed that

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Expression of matrix metalloproteinase-2 in the extracellular matrix of osseointegrated and diseased implants
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Background: Recently with improvement of dental implantology science, osseointegrated implants show a considerable durability, however; failures are not completely avoidable. Matrix metalloproteinase-2 (MMP-2) expression is disturbed in many pathological conditions such as peri-implantitis and periodontitis. This study was carried out to investigate the tissue expression of MMP-2 in the extracellular matrix of osseointegrated and diseased implants. Subjects and methods: Gingival biopsies were collected from six patients having osseointegrated or working implants and twenty with diseased or non osseointegrated implants and (6) controls having no implants. In situ hybridization technique was used to analyze the changes in immunoreactivity of

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Thu Jun 01 2017
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New mini dental implant attachments versus O-ring attachment after cyclic aging: Analysis of retention strength and gap space
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A Hypothesis of Architectural Environment Exercise for Actor Training (Continuous exercise space workshop – A model): هيثم عبد الرزاق علي
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The peculiarity of the theater does not lie in its dramatic content because many literary genres and other artistic styles share with it in this content. The peculiarity of the theater lies in contemplating the drama through what is architectural, and this architectural axis is what distinguishes its character. It is a spatial poetry which is composed by the laws of physics and chemistry, (Weight, height, distance, rhythm, gravity, impulses and chemical excretions). i.e., what cannot be expressed in words. This is a game of space to exchange and organize energy and communicate in space by the living body, which contains the possibilities of the living drawing in space: in the time and place. This research deals with the importance of the

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Effect of physical form and washing of treated and untreated rice straw with sodium hydroxide upon chemical composition and in vitro digestibility
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Hydroxide upon the chemical composition and dry matter(DM) and organic matter(OM) digestibility . Rice straw was treated with 4% sodium hydroxide using 30% of DM basis moisture, and incubated at 40 ºC for 40 days., DM digestibility (DMD) was significantly affected (P<0.01) by the treatment , where DMD increased The objective of this experiment was to study the effect of physical form (long ,chopped and ground ) and washing rice straw treated with sodium from 42.32 to 45.41% , OM digestibility (OMD) and total digestible nutrient (TDN) increased(P<0.05) from 47.38 and 49.33 to 49.67 and 52.83% ,respectively. While hemicellulose content increased (P<0.05 ) from 261.71 to 268.17 gm/kg DM ,and metabolizable energy (ME) from 7.11 to 7.48 MJ/

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Consequences for the groups 𝒮𝓛(2,𝒰), 𝒰 = 23 and 29
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On The Nearby-Tip Strain Investigation and Failure-Propability Evaluation for Impacted Thin Plates Using the 2-Random-Variables Multi-Canonical-Based Joint Propability Distributions
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The study of the validity and probability of failure in solids and structures is highly considered as one of the most incredibly-highlighted study fields in many science and engineering applications, the design analysts must therefore seek to investigate the points where the failing strains may be occurred, the probabilities of which these strains can cause the existing cracks to propagate through the fractured medium considered, and thereafter the solutions by which the analysts can adopt the approachable techniques to reduce/arrest these propagating cracks.In the present study a theoretical investigation upon simply-supported thin plates having surface cracks within their structure is to be accomplished, and the applied impact load to the

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Publication Date
Wed Jun 03 2015
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Synthesis, characterization and Antibacterial of 2, 3 Dihydrobenzo Thiazole -2- Carboxylic acid complexes with some selected Metal ions.
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