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kent1178311591.pdf (346.62 KB)
ETD Abstract Container
Abstract Header
Examining the Absolute Rate of Convergence of Summability Assisted Fourier Series
Author Info
Wright, Brian M.
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=kent1178311591
Abstract Details
Year and Degree
2007, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
Abstract
Let f be a 2-π periodic function which is of bounded variation over the interval [-π, π], and let S
n
(f,x) denote the partial sums of the Fourier series of f. If H
Φ
= (h
n
,k) is a regular Hausdorff summability method generated by the weight function, Φ (t), we provide a bound for the absolute rate of convergence of the transform, (H
Φ
S)
n
, and show that this bound is sharp in the sense that it cannot be improved without further assumptions. We also show that the rate of convergence is affected by the total variation of the rows of the summability method. Finally, we extend our results to find a bound for the two-variable case, and again show that the given bound is sharp.
Committee
Kazim Khan (Advisor)
Pages
60 p.
Subject Headings
Mathematics
Keywords
Fourier series convergence,
;
summability methods
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Citations
Wright, B. M. (2007).
Examining the Absolute Rate of Convergence of Summability Assisted Fourier Series
[Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1178311591
APA Style (7th edition)
Wright, Brian.
Examining the Absolute Rate of Convergence of Summability Assisted Fourier Series.
2007. Kent State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=kent1178311591.
MLA Style (8th edition)
Wright, Brian. "Examining the Absolute Rate of Convergence of Summability Assisted Fourier Series." Doctoral dissertation, Kent State University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=kent1178311591
Chicago Manual of Style (17th edition)
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Document number:
kent1178311591
Download Count:
847
Copyright Info
© 2007, all rights reserved.
This open access ETD is published by Kent State University and OhioLINK.