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kent1272312534.pdf (284.5 KB)
ETD Abstract Container
Abstract Header
On Sylvester's Theorem
Author Info
Hanchin, Terence G.
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=kent1272312534
Abstract Details
Year and Degree
2010, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
Abstract
Variation-diminishing convultion transforms have proven useful in a variety of areas of mathematics. A theorem of J.J. Sylvester on sums of shifted monomials, when extended to the context of convolution on the real line, shows that monomial kernels exhibit properties that are nearly variation-diminishing. We call these related properties
even variation-diminishing
and
odd variation-diminishing
. We demonstrate methods for generating further examples of even and odd variation-diminishing kernels, and ultimately provide a characterization of such kernels in terms of their translation determinants. We also show how the even and odd variation-diminishing properties of a particular class of kernels lead to the fact that convolution on the circle with certain generalized de la Vallée Poussin polynomials is a cyclic variation-diminishing linear transformation.
Committee
Dr. Alfred Cavaretta (Committee Chair)
Dr. Artem Zvavitch (Committee Member)
Dr. Volodymyr Andriyevskyy (Committee Member)
Dr. Victor Lomonosov (Committee Member)
Dr. Elizabeth Mann (Committee Member)
Dr. James Gleeson (Committee Member)
Pages
61 p.
Subject Headings
Mathematics
Keywords
variation diminishing
;
convolution
;
de la vallee poussin
Recommended Citations
Refworks
EndNote
RIS
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Citations
Hanchin, T. G. (2010).
On Sylvester's Theorem
[Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1272312534
APA Style (7th edition)
Hanchin, Terence.
On Sylvester's Theorem.
2010. Kent State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=kent1272312534.
MLA Style (8th edition)
Hanchin, Terence. "On Sylvester's Theorem." Doctoral dissertation, Kent State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=kent1272312534
Chicago Manual of Style (17th edition)
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Document number:
kent1272312534
Download Count:
1,095
Copyright Info
© 2010, all rights reserved.
This open access ETD is published by Kent State University and OhioLINK.