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MRbmuIoBVTCNdQwCLKT9
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 May 01 2021
Journal Name
Journal Of Physics: Conference Series
The substitutions of Strontium by yttrium and their effects on Bi<sub>2</sub>Sr<sub>2</sub>-<sub>x</sub>Y<sub>x</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10</sub>+<sub>δ</sub> superconducting compound
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Abstract<p>Superconducting compound Bi<sub>2</sub>Sr2-<sub>x</sub>Y<sub>x</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10+δ</sub> were Synthesized by method of solid state reaction, at 1033 K for 160 hours temperature of the sintering at normal atmospheric pressure where substitutions Yttrium oxide with Strontium. When Y2O3 concentration (0.0, 0.1, 0.2, 0.3, 0.4 and 0.5). All specimens of Bi<sub>2</sub>Sr<sub>2</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10+δ</sub> superconducting compounds were examined. The resistivity of electrical was checked by the four point probe technique, It was found th</p> ... Show More
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Publication Date
Mon Apr 01 2024
Journal Name
Indonesian Journal Of Chemistry
Synthesis, Structure and Biological Activity Studies of New Metal Ion Complexes Based on 3-[(3-Hydroxynaphthalene-2-yl-ethylidene)-hydrazono]-1,3-dihydro-indol-2-one
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In the present study, a novel ligand (L) made of 2-hydroxynaphthaldehyde and 3-hydrazone-1,3-dihydro-indole-2-one(3-[(3-hydroxynaphthalen-2-yl-ethylidene)-hydrazono]-1,3-dihydro-indol-2-one). The ligand was characterized by FTIR, UV-vis, mass, 1H-NMR, 13C-NMR, and CHN elemental analysis. New complexes of this ligand were created by treating methanol and a drop of DMF solution of the produced ligand with the hydrated metal salts of Mn(II), Co(II), Ni(II), Cu(II), and Zn(II) in a molar ratio of 2:1 (L:M). As a result, complexes have been emerged and identified FTIR, UV-vis, C.H.N., chloride-containing, molar conductance, magnetic susceptibility, and atomic absorption. The characterization result for each complex indicated complexes wi

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Publication Date
Wed Dec 30 2015
Journal Name
College Of Islamic Sciences
Achieve breastfeeding book and theft book To the end of the door cut the way of the manuscript Sailing Forum for Sheikh Ibrahim bin Mohammed Halabi (T: 659 H): Study and achieve
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Achieve breastfeeding book and theft book
To the end of the door cut the way of the manuscript
Sailing Forum for Sheikh Ibrahim bin Mohammed Halabi
(T: 659 H)

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Publication Date
Mon Dec 29 1997
Journal Name
كلية العلوم للبنات
Synthesis And Studies Of Complexes Of Some Elements With 2-Mercaptohiazole (2-HMBT)
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Synthesis And Studies Of Complexes Of Some Elements With 2-Mercaptohiazole (2-HMBT)

Publication Date
Wed Nov 12 2025
Journal Name
Journal Of Baghdad College Of Dentistry
Effect of Periodontal Therapy on Serum and Salivary Interleukin-2 Levels in Chronic Periodontitis
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Background: Interleukine-2 is a multifunctional cytokine, considered a central regulator of host resistance against a variety of pathogens and has been recently demonstrated to exert an active role in the pathogenesis of periodontal diseases. The purpose of this study was to evaluate the effect of scaling and root planning on level of IL-2 in serum and saliva of patients with chronic generalized periodontitis, in relation to clinical parameters. Materials and Methods: A total of 50 subjects were enrolled, of which 25 had chronic generalized periodontitis and 25 periodontally healthy subjects as control. The clinical parameters included: gingival index, pocket probing depth, clinical attachment level and bleeding on probing. The level of

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Publication Date
Tue Nov 03 2015
Journal Name
Journal Of Natural Sciences Research
Implementation of remote sensing for vegetation studying using vegetation indices and automatic feature space plot
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Publication Date
Fri May 31 2024
Journal Name
Journal Of Interdisciplinary Mathematics
Fibrewise locally micro sliceable and fibrewise locally micro-section able micro-topological space
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The primary objective of this research be to develop a novel thought of fibrewise micro—topological spaces over B. We present the notions from fibrewise micro closed, fibrewise micro open, fibrewise locally micro sliceable, and fibrewise locally micro-section able micro topological spaces over B. Moreover, we define these concepts and back them up with proof and some micro topological characteristics connected to these ideas, including studies and fibrewise locally micro sliceable and fibrewise locally micro-section able micro topological spaces, making it ideal for applications where high-performance processing is needed. This paper will explore the features and benefits of fibrewise locally micro-sliceable and fibrewise locally

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Publication Date
Wed Dec 01 2021
Journal Name
Baghdad Science Journal
New Common Fixed Points for Total Asymptotically Nonexpansive Mapping in CAT(0) Space
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      Strong and ∆-convergence for a two-step iteration process utilizing asymptotically nonexpansive and total asymptotically nonexpansive noneslf mappings in the CAT(0) spaces have been studied. As well, several strong convergence theorems under semi-compact and condition (M) have been proved. Our results improve and extend numerous familiar results from the existing literature.

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Publication Date
Fri Dec 19 2014
Journal Name
Al-mustansiriyah
Synthesis, Spectroscopic and Antibacterial Studies of N (2-amino phenyl)-N-((pyridine-2-yl) methyl) Benzene-1, 2-Diamine Complexes
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Publication Date
Mon Dec 01 2014
Journal Name
Journal Of Economics And Administrative Sciences
Material Requirements Planning (MRP) for Electric Geyser Product by Using Goal Programming\ applicative research in the general company of electrical industrialization
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Material Requirements Planning System (MRP) is considered as one of the planning and controlling of production and inventory systems which is used to prepare plan of the final production requirements and its parts of subcomponents raw materials and the time at which it was needed for the purpose of preparing orders of production and purchase.

The problem of the present work is represented in the general company of electrical industrialization adoption of traditional methods and personal experience of the process of the products and\or purchase quantity and inventory quantities and limiting the required time for acquiring the required quantities of the materials and parts used in the finish product of the

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