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VIDEO LIBRARY |
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Complex orthogonality H. Stahl Technische Fachhochschule Berlin |
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Abstract: The great majority of research contributions in the field of orthogonal polynomials is concerned with concepts that live either on the real axis \begin{equation} \int \bar z^jp_n(z)\,d\mu(z)=0\quad\text{for}\quad j=0,\dots,n-1, \tag{1} \end{equation} where In several areas of rational approximation, like in Padé approximation, rational approximation, and also in the theory of continued fractions, we are confronted with orthogonality relations that no longer are Hermitian. Here, the relations may typically have a form like \begin{equation} \int_\gamma z^jp_n(z)f(z)\,dz=0\quad\text{for}\quad j=0,\dots,n-1, \tag{2} \end{equation} with After the discussion of some examples and some glances at the background of the problem in approximation theory, we will review concepts for the asymptotic analysis of sequences of orthogonal polynomials Language: English |