published_or_final_version / Mathematics / Master / Master of Philosophy

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This thesis is an analysis of convergence results on Fourier series. Convergence of Fourier series is studied in two ways in this thesis. The first way is in the context of Banach spaces, where the set of functions is restricted to a certain Banach space. Then the problem is in determining whether the Fourier series of a function can be represented as an element of that Banach space. The second way is in the context of pointwise convergence. Here, the problem is in determining what conditions need to be placed on an arbitrary function for its Fourier series to converge at a point.

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Zugl.: Karlsruhe, Univ., Diss., 2006

Thesis (Ph. D.)--University of Wisconsin, 1967. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (doctoral)--University of Tartu, 2006. / This dissertation is based on 3 papers.

BENJAMIM FILHO, Francisco de Assis. Desigualdades isoperimétricas para integrais de curvatura em domínios k-convexos estrelados. 2011. 61 f. Dissertação (Mestrado em Matemática)- Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2011. / Submitted by Rocilda Sales (rocilda@ufc.br) on 2011-11-17T17:18:59Z No. of bitstreams: 1 2011_dis_fabfilho.pdf: 425056 bytes, checksum: 6f08bf20bf495faeb5edceec320609b2 (MD5) / Approved for entry into archive by Rocilda Sales(rocilda@ufc.br) on 2011-11-18T13:08:51Z (GMT) No. of bitstreams: 1 2011_dis_fabfilho.pdf: 425056 bytes, checksum: 6f08bf20bf495faeb5edceec320609b2 (MD5) / Made available in DSpace on 2011-11-18T13:08:51Z (GMT). No. of bitstreams: 1 2011_dis_fabfilho.pdf: 425056 bytes, checksum: 6f08bf20bf495faeb5edceec320609b2 (MD5) Previous issue date: 2011 / Based on the work of Gerhardt and Urbasa [12], [36], we prove a global convergence result and precisely determine the asymptotic behavior of solutions of a geometric flow describing the evolution of starshaped, k-convex hypersurfaces according to certain functions of the principal curvatures. As an application, and following the argument of Guan and Li [16], we use a special case of this convergence result to generalize the classical Alexandrov-Fenchel inequality for domains starry and k-convex. / Baseados nos trabalhos De Gerhardt e Urbas [12], [36], provamos um resultado de convergência global e determinamos precisamente o comportamento assintótico de soluções de um fluxo geométrico que descreve a evolução de hipersuperfícies estreladas e k-convexas por funções das curvaturas principais. Como aplicação, e seguindo o argumento de Guan e Li [16], utilizamos um caso particular deste resultado de convergência para generalizar a clássica desigualdade de Alexandrov-Fenchel para domínios estrelados e k-convexos.