Convergence properties of one and multidimensional trigonometric Fourier series

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dc.contributor.advisorTamás, Gát György
dc.contributor.authorAllauca Guananga , Steven Gerónimo
dc.contributor.departmentDE--Természettudományi és Technológiai Kar--Matematikai Intézet
dc.date.accessioned2025-02-03T08:19:01Z
dc.date.available2025-02-03T08:19:01Z
dc.date.created2024-05-01
dc.description.abstractIn this work, first of all, we study the convergence properties of one and multidimensional trigonometric Fourier series. It begins by discussing fundamental concepts such as vec- tor spaces, function spaces, and interpolation theorems. Inspired by Fourier analysis, it explores the feasibility of extending these concepts to infinite-dimensional spaces and or- thonormal systems. The study extensively covers the convergence behavior of Fourier series in the one-dimensional case, including partial sums, Dirichlet kernels, Fourier coefficients, and convergence criteria. It also examines the concept of Fej´er means. In the multidi- mensional context, the thesis explores topics such as partial sums, norm convergence, and summability means. Throughout the thesis, we use and refer to books [1] and [2], as well as the lectures given by my supervisor in his ”Fourier series” lectures [3]. What results are not directly referred to are taken from lectures [3, 4]. No new statements or results have been formulated in the thesis.
dc.description.courseMS.c. Applied mathematics
dc.description.degreeMSc/MA
dc.format.extent56
dc.identifier.urihttps://hdl.handle.net/2437/386376
dc.language.isoen
dc.rights.accessHozzáférhető a 2022 decemberi felsőoktatási törvénymódosítás értelmében.
dc.subjectFourier series
dc.subjectDirichlet kernels
dc.subjectFejér means
dc.subjectSummability means
dc.subject.dspaceMathematics
dc.titleConvergence properties of one and multidimensional trigonometric Fourier series
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