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Djinja, Domingos
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School of Education, Culture and Communication
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Mathematical Analysis
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Construction of Representations of Commutation Relations by Linear Operators in Banach SpacesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2023 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Västerås: Mälardalens universitet, 2023.
##### Series

Mälardalen University Press Dissertations, ISSN 1651-4238 ; 382
##### National Category

Mathematical Analysis
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

URN: urn:nbn:se:mdh:diva-62303ISBN: 978-91-7485-594-4 (print)OAI: oai:DiVA.org:mdh-62303DiVA, id: diva2:1751898
##### Public defence

2023-05-29, Kappa, Mälardalens universitet, Västerås, 13:15 (English)
##### Opponent

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##### Funder

Sida - Swedish International Development Cooperation AgencyAvailable from: 2023-04-20 Created: 2023-04-19 Last updated: 2023-05-08Bibliographically approved
##### List of papers

This thesis is devoted to the construction and investigation of some properties of pairs of linear operators (A, B) (representations) satisfying commutation relations AB=BF(A), where F denotes certain polynomial. Commutation relations of this kind are called "covariance type" and finding their representations is equivalent to solving operator equations. This kind of commutation relations and operator representations on finite-dimensional or infinite-dimensional linear spaces are important in Physics, Engineering and many areas of Mathematics. The most original part of the present thesis contains the construction of representations of commutation relations AB=BF(A) by linear integral operators, multiplication operators and weighted composition operators defined on Banach spaces of continuous functions, on L_{p} spaces and l_{p} spaces. Conditions on kernels of integral operators and functions defining multiplication and composition operators are derived for these operators to satisfy the covariance type commutation relations, both for the general polynomials F and for important specific choices of F. These conditions are used for construction of various concrete pairs of operators satisfying such commutation relations. Many essential algebraic properties of commutation relations are studied here as well.

1. Representations of polynomial covariance type commutation relations by linear integral operators on L_{p} over measure spaces$(function(){PrimeFaces.cw("OverlayPanel","overlay1722884",{id:"formSmash:j_idt563:0:j_idt567",widgetVar:"overlay1722884",target:"formSmash:j_idt563:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Linear integral operators on L_{p} spaces representing polynomial covariance type commutation relations$(function(){PrimeFaces.cw("OverlayPanel","overlay1751883",{id:"formSmash:j_idt563:1:j_idt567",widgetVar:"overlay1751883",target:"formSmash:j_idt563:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Representations of polynomial covariance type commutation relations by linear integral operators with general separable kernels in L_{p} spaces$(function(){PrimeFaces.cw("OverlayPanel","overlay1751885",{id:"formSmash:j_idt563:2:j_idt567",widgetVar:"overlay1751885",target:"formSmash:j_idt563:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Multiplication and linear integral operators in L_{p} spaces representing polynomial covariance type commutation relations$(function(){PrimeFaces.cw("OverlayPanel","overlay1751892",{id:"formSmash:j_idt563:3:j_idt567",widgetVar:"overlay1751892",target:"formSmash:j_idt563:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Representations of polynomial covariance type commutation relations by piecewise function multiplication and composition operators$(function(){PrimeFaces.cw("OverlayPanel","overlay1751893",{id:"formSmash:j_idt563:4:j_idt567",widgetVar:"overlay1751893",target:"formSmash:j_idt563:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

6. Some algebraic properties of representations of polynomial covariance type commutation relations$(function(){PrimeFaces.cw("OverlayPanel","overlay1751894",{id:"formSmash:j_idt563:5:j_idt567",widgetVar:"overlay1751894",target:"formSmash:j_idt563:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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