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kent1270503593.pdf (268.13 KB)
ETD Abstract Container
Abstract Header
Geometric Properties of Orbits of Integral Operators
Author Info
Beil, Joel S.
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=kent1270503593
Abstract Details
Year and Degree
2010, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
Abstract
This dissertation addresses some of the geometric properties of orbits of integral operators on the Banach spaces C[0, 1] and L
p
[0, 1]. It will be shown that, under very general conditions on the starting element, an orbit of the Volterra operator cannot be a Schauder basis for its closed linear span. However, lacunary subsequences of the orbit will be seen to be Schauder bases for their closed linear span. Bounds on the norm of the iterates and a monotonicity result for a certain class of functions will be established. Moreover, exact asymptotic constants arising from the analysis will be exhibited.
Committee
Per Enflo, PhD (Committee Chair)
Victor Lomonosov, PhD (Committee Member)
Artem Zvavitch, PhD (Committee Member)
Thomas Janson, PhD (Committee Member)
Khandker Quader, PhD (Committee Member)
Pages
53 p.
Subject Headings
Mathematics
Keywords
integral operators
;
Schauder bases
;
operator orbits
;
lacunary subsequences
;
asymptotic analysis
Recommended Citations
Refworks
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Citations
Beil, J. S. (2010).
Geometric Properties of Orbits of Integral Operators
[Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1270503593
APA Style (7th edition)
Beil, Joel.
Geometric Properties of Orbits of Integral Operators.
2010. Kent State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=kent1270503593.
MLA Style (8th edition)
Beil, Joel. "Geometric Properties of Orbits of Integral Operators." Doctoral dissertation, Kent State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=kent1270503593
Chicago Manual of Style (17th edition)
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Document number:
kent1270503593
Download Count:
540
Copyright Info
© 2010, all rights reserved.
This open access ETD is published by Kent State University and OhioLINK.