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Compactness properties of Volterra-type integral operators on analytic function spaces
No full textThe topic of this dissertation lies at the intersection of analytic function theory and operator theory. In the thesis, compactness and structural properties of a class of Volterra-type (integral) operators acting on analytic function spaces are investigated. The Volterra-type operator is obtained by integrating a product of two analytic functions, where one of these functions, the so-called symbol of the operator, is fixed and the other one is considered to be a variable. This integral operator was introduced by C. Pommerenke in 1977 in connection to exponential integrability of BMOA-functions. A systematic research of Volterra-type operators was initiated by Aleman and Siskakis in the mid-1990s when they characterized the boundedness and compactness of these operators on the Hardy spaces and weighted Bergman spaces.
In the first article of the thesis, we derive estimates for the essential and weak essential norms of a Volterra-type operator in terms of its symbol when the operator is acting on the Hardy spaces, BMOA and VMOA. The essential and weak essential norms of a linear operator are its distances from compact and weakly compact operators respectively. In particular, it follows from our estimates that the compactness and weak compactness of Volterra-type operator coincide when its domain is the non-reflexive Hardy space, BMOA, or VMOA.
In the second article, a notion of strict singularity of a linear operator is investigated in the case of the Volterra-type operator acting on the Hardy spaces. An operator between Banach spaces is strictly singular if its restriction to any closed infinite-dimensional subspace is not a linear isomorphism onto its range. We construct an isomorphic copy M of the sequence space of p-summable sequences and show that a non-compact Volterra-type operator restricted to M is a linear isomorphism onto its range. This implies that the strict singularity and compactness of this operator coincide in the Hardy space case.
In the third article, we provide estimates for the operator norms and essential norms of the Volterra-type operator acting between weighted Bergman spaces, where the weight function satisfies a doubling condition.Väitöskirja kuuluu operaattoriteorian ja kompleksianalyysin alaan. Työssä tarkastellaan Volterra-tyyppisiä lineaarisia integraalioperaattoreita ja niiden kompaktisuusominaisuuksia. Kyseisen operaattorin esitteli Pommerenke vuonna 1977 ns. BMOA-funktioiden eksponentiaalisen integroituvuuden yhteydessä. Volterra-tyyppinen operaattori esiintyy usealla matemaattisen analyysin alalla kuten kompositio-operaattoreiden puoliryhmien teorian yhteydessä. Operaattorin systemaattisen tutkimuksen aloitti Aleman ja Siskakis yhteistyökumppaneineen 1990-luvun puolivälissä karakterisoimalle sen rajoittuneisuuden ja kompaktisuuden Hardy-ja Bergman-avaruuksilla.
Väitöskirjassa johdetaan estimaatteja Volterra-tyyppisen operaattorin etäisyydelle kompaktien ja heikosti kompaktien operaattoreiden ideaaleista sen symbolin avulla ilmaistuna. Näistä arvioista seuraa esimerkiksi kyseisen operaattorin kompaktisuuden ja heikon kompaktisuuden yhtäpitävyys tiettyjen funktio-avaruuksien tapauksissa. Lisäksi työssä osoitetaan, että Hardy-avaruuksilla määritellyn Volterra-tyyppisen operaattorin rajoittuma eräälle p-summautuvien jonojen avaruuden kanssa isomorfiselle aliavaruudelle on alhaalta rajoitettu. Tästä seuraa erityisesti, että tämän operaattorin aito singulaarisuus ja kompaktisuus ovat yhtäpitäviä Hardy-avaruuden tapauksessa.ei saavutettav
Strict singularity of a Volterra-type integral operator on H^p
Get PDFWe consider a Volterra-type integral operator acting on the Hardy spaces H^p of the unit disc. The operator T_g was introduced by Ch. Pommerenke and it has been studied systematically by several people including A. Aleman, A.G. Siskakis and R. Zhao among others. From a functional analytic point of view, one interesting notion is the strict singularity of a linear operator between Banach spaces. An operator is strictly singular if its restriction to any infinite-dimensional subspace is not an isomorphism onto its range. We discuss our recent result, which states that a non-compact T_g fixes an isomorphic copy of the sequence space l^p. In particular, the strict singularity of T_g coincides with its compactness on spaces H^p
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Toeplitz operators with piecewise continuous symbols on the Hardy space H 1
No full textThe geometric descriptions of the (essential) spectra of Toeplitz operators with piecewise continuous symbols are among the most beautiful results about Toeplitz operators on Hardy spaces with . In the Hardy space , the essential spectra of Toeplitz operators are known for continuous symbols and symbols in the Douglas algebra . It is natural to ask whether the theory for piecewise continuous symbols can also be extended to . We answer this question in negative and show in particular that the Toeplitz operator is never bounded on if its symbol has a jump discontinuity
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
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koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
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