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Gaussian structures and orthogonal polynomials

<p>This thesis consists of four papers on the following topics in analysis and probability: analysis on Wiener space, asymptotic properties of orthogonal polynomials, and convergence rates in the central limit theorem. The first paper gives lower bounds on the constants in the Meyer inequality from the Malliavin calculus. It is shown that both constants grow at least like <i>(p-1)</i><sup>-1</sup> or like <i>p</i> when <i>p</i> approaches 1 or ∞ respectively. This agrees with known upper bounds. In the second paper, an extremal problem on Wiener chaos motivates an investigation of the <i>L</i><sup>p</sup>-norms of Hermite polynomials. This is followed up by similar computations for Charlier polynomials in the third paper. In both cases, the <i>L</i><sup>p</sup>-norms present a peculiar behaviour with certain threshold values of p, where the growth rate and the dominating intervals undergo a rapid change. The fourth paper analyzes a connection between probability and numerical analysis. More precisely, known estimates on the convergence rate of finite difference equations are "translated" into results on convergence rates of certain functionals in the central limit theorem. These are also extended, using interpolation of Banach spaces as a main tool. Besov spaces play a central role in the emerging results.</p>

Identiferoai:union.ndltd.org:UPSALLA/oai:DiVA.org:uu-1632
Date January 2002
CreatorsLarsson-Cohn, Lars
PublisherUppsala University, Mathematics, Uppsala : Avdelningen för matematik
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeDoctoral thesis, comprehensive summary, text
RelationUppsala Dissertations in Mathematics, 1401-2049 ; 22

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