Spaces of harmonic functions and harmonic quasiconformal mappings

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Spaces of harmonic functions and harmonic quasiconformal mappings

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dc.contributor.advisor Arsenović, Miloš
dc.contributor.author Shkheam, Abejela
dc.date.accessioned 2013-10-08T10:30:48Z
dc.date.available 2013-10-08T10:30:48Z
dc.date.issued 2013
dc.identifier.uri http://hdl.handle.net/123456789/3053
dc.description.abstract This thesis has been written under the supervision of my mentor, Prof. dr. Milo s Arsenovi c at the University of Belgrade academic, and my co-mentor dr. Vladimir Bo zin in year 2013. The thesis consists of three chapters. In the rst chapter we start from de nition of harmonic functions (by mean value property) and give some of their properties. This leads to a brief discussion of homogeneous harmonic polynomials, and we also introduce subharmonic functions and subharmonic behaviour, which we need later. In the second chapter we present a simple derivation of the explicit formula for the harmonic Bergman reproducing kernel on the ball in euclidean space and give a proof that the harmonic Bergman projection is Lp bounded, for 1 < p < 1, we furthermore discuss duality results. We then extend some of our previous discussion to the weighted Bergman spaces. In the last chapter, we investigate the Bergman space for harmonic functions bp, 0 < p < 1 on RnnZn. In the planar case we prove that bp 6= f0g for all 0 < p < 1. Finally we prove the main result of this thesis bq bp for n=(k + 1) q < p < n=k, (k = 1; 2; :::). This chapter is based mainly on the published paper [44]. M. Arsenovi c, D. Ke cki c,[5] gave analogous results for analytic functions in the planar case. In the plane the logarithmic function log jxj, plays a central role because it makes a di erence between analytic and harmonic case, but in the space the function jxj2􀀀n; n > 2 hints at the contrast between harmonic function in the plane and in higher dimensions. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2013-10-08T10:30:48Z No. of bitstreams: 1 phd_Shkheam_Abejela.pdf: 650609 bytes, checksum: 18616d82fae5cce58bc52e5b6600a563 (MD5) en
dc.description.provenance Made available in DSpace on 2013-10-08T10:30:48Z (GMT). No. of bitstreams: 1 phd_Shkheam_Abejela.pdf: 650609 bytes, checksum: 18616d82fae5cce58bc52e5b6600a563 (MD5) Previous issue date: 2013 en
dc.format.mimetype PDF en_US
dc.language.iso en en_US
dc.title Spaces of harmonic functions and harmonic quasiconformal mappings en_US
mf.author.birth-date 1975-12-28
mf.author.birth-place Zawia en_US
mf.author.birth-country Libya en_US
mf.author.residence-state Libya en_US
mf.author.citizenship Libyan en_US
mf.author.nationality Libyan en_US
mf.subject.area Matematika en_US
mf.subject.subarea Kompleksna Analiza en_US
mf.contributor.committee Božin, Vladimir
mf.contributor.committee Mateljević, Miodrag
mf.contributor.committee Manojlović, Vesna
mf.contributor.committee Mihić, Olivera
mf.university.faculty Mathematical en_US
mf.document.references 47 en_US
mf.document.pages 64 en_US
mf.document.location Beograd en_US
mf.document.genealogy-project No en_US
mf.author.parent Salem en_US
mf.university Belgrade en_US

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