Absolute Norlund summability of Fourier series

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dc.contributor.advisorUrsell, H. D.
dc.contributor.authorGoel, D. S. (Devendra Swarup)
dc.date.accessioned2005-07-15T20:00:30Z
dc.date.available2005-07-15T20:00:30Z
dc.date.issued1969
dc.descriptionBibliography: p. 62-63.en
dc.description.abstractIn this thesis we examine the properties of the absolute Norlund Summability (ANS) method and its application to Fourier Series of a function f(x), periodic with period 2π and integrable L. In chapter II we discuss the various consistency theorems for ANS. Chapter III consists of a theorem on the ANS of Fourier Series of a function f(x) belonging to the class Lip α. Chapter IV contains a result on the ANS of Fourier Series when ∅(t)= ½{f(x-t)} is of bounded variation in the interval (O, π). In 1959 Varshney [16] proved a theorem on the absolute harmonic summability of a series related to Fourier Series of f(x) when ϕ(t) is of bounded variation in the interval (O,π). In Chapter V we prove a theorem on the ANS of Fourier Series when cp(t) is of bounded variation which generalises the result on absolute harmonic summability due to Varshney and includes the result given in Chapter IV. In Chapter VI we prove a theorem on the ANS of Fourier Series under the condition φ(□(1/t))|ϕ(t)| = 0(1) where φ(n) is a monotonic increasing function.en
dc.description.notesThis title is not available online. Access options are: - consulting the copy from Archives in our reading room in person - https://asc.ucalgary.ca/visiting/ - borrowing a circulating copy from the Library catalogue – https://ucalgary.primo.exlibrisgroup.com/discovery/search?vid=01UCALG_INST:UCALGARY&lang=en
dc.format.extentvi, 73 leaves ; ill. ; 30 cm.en
dc.identifier82481521en
dc.identifier.citationGoel, D. S. (1969). Absolute Norlund summability of Fourier series (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/22960en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/22960
dc.identifier.lccQA 404 G62 1969en
dc.identifier.otherBarcode: 82481521en
dc.identifier.urihttp://hdl.handle.net/1880/1933
dc.language.isoeng
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subject.lccQA 404 G62 1969en
dc.subject.lcshFourier series
dc.titleAbsolute Norlund summability of Fourier series
dc.typemaster thesis
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameMaster of Science (MSc)
ucalgary.thesis.accessionTheses Collection 58.002:Box 44 82481521
ucalgary.thesis.notesPLen
ucalgary.thesis.uarcreleasenoen
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