Ursell, H. D.Goel, D. S. (Devendra Swarup)2005-07-152005-07-151969Barcode: 82481521http://hdl.handle.net/1880/1933Bibliography: p. 62-63.In 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.vi, 73 leaves ; ill. ; 30 cm.engUniversity 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.QA 404 G62 1969Fourier seriesmaster thesis10.11575/PRISM/22960QA 404 G62 1969