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Finite Blaschke products versus polynomialsTsang, Chiu-yin, 曾超賢 January 2012 (has links)
The objective of the thesis is to compare polynomials and finite Blaschke products, and demonstrate that they share many similar properties and hence we can
establish a dictionary between these two kinds of finite maps for the first time.
The results for polynomials were reviewed first. In particular, a special kind of
polynomials was discussed, namely, Chebyshev polynomials, which can be defined
by the trigonometric cosine function cos ?. Also, a complete classification for two
polynomials sharing a set was given.
In this thesis, some analogous results for finite Blaschke products were proved.
Firstly, Chebyshev-Blaschke products were introduced. They can be defined by re-
placing the trigonometric cosine function cos z by the Jacobi cosine function cd(u; ? ).
They were shown to have several similar properties of Chebyshev polynomials, for
example, both of them share the same monodromy, satisfy some differential equations and solve some minimization problems. In addition, some analogous results
about two finite Blaschke products sharing a set were proved, based on Dinh's and
Pakovich's ideas.
Moreover, the density of prime polynomials was investigated in two different
ways: (i) expressing the polynomials of degree n in terms of the zeros and the leading
coefficient; (ii) expressing the polynomials of degree n in terms of the coefficients.
Also, the quantitative version of the density of composite polynomials was developed
and a density estimate on the set of composite polynomials was given. Furthermore,
some analogous results on the the density of prime Blaschke products were proved. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy
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The Blaschke-Santalo inequalityVan Wyk, Hans-Werner. January 2007 (has links)
Thesis (M.Sc.(Mathematics and Applied Mathematics)) -- Universiteit van Pretoria, 2007. / Includes bibliographical references. Available on the Internet via the World Wide Web.
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The Blaschke-Santaló inequalityVan Wyk, Hans-Werner 11 June 2008 (has links)
No abstract available / Dissertation (MSc (Mathematics))--University of Pretoria, 2008. / Mathematics and Applied Mathematics / unrestricted
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Nonlinear approximation using Blaschke polynomialsVan Vliet, Daniel, January 1900 (has links)
Thesis (Ph. D.)--West Virginia University, 2007. / Title from document title page. Document formatted into pages; contains x, 92 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 75-76).
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